### Interview by **Dr Houry Melkonian.**

### The interview includes extracts from Prof Ringrose’s talk at the 50th anniversary of the NBFAS.

*John Ringrose spent most of his academic career in the Mathematics Department at Newcastle University. His main research interests were in operator algebras – first, in nest algebras, then turning to C*- algebras and, especially, von-Neumann algebras. A large part of the latter work was carried out in collaboration with R. V. Kadison, and concerned the cohomology theory of such algebras.*

**How would you describe the early growth of study and research in functional analysis within the British mathematical community? **

As I see it, the early growth of study and research in functional analysis in Britain is very largely dependent on two people. It is “a tale of two Franks’’: Frank Smithies and Frank Bonsall. Of course, there are quite a few other people – far too many to mention in a brief interview – who made significant contributions. Nevertheless, I think it was the “two Franks’’ that were the primary influence.

Frank Smithies grew up in Edinburgh. In 1927, aged just 15, he entered the university there. He graduated four years later, top of the honours mathematics class. He then went on to Cambridge, where he took two years of advanced undergraduate lectures, followed by three years of research leading to his Ph.D. His research supervisor was the great classical analyst G. H. Hardy. He spent two years at the Institute for Advanced Study in Princeton, and in 1938, returned to Cambridge. Apart from a few years of scientific war work during World War II, he was based in Cambridge for the rest of his life.

His interest in Functional Analysis was first aroused at a meeting of the St. John’s College undergraduate mathematical society. The talk was at popular level; the subject was essentially Hilbert space theory with the speaker S. W. P. Steen. In later years, Steen became a specialist in mathematical logic, but in the 1930s he wrote a paper on Hilbert space operator algebras. It was this “popular” lecture by Steen that got Smithies thinking about functional analysis. His interest was strengthened, a year or two later, when Von-Neumann visited Cambridge and gave some lectures. G. H. Hardy had a marked aversion towards all things abstract in mathematics; nevertheless, and to his credit, he encouraged Smithies to extend his knowledge of abstract analysis, inter alia by reading the (then) recently published treatises of Stefan Banach and Marshal Stone.

In terms of published work, Smithies had two main phases. Up to the early 1940s there was a lot of classical analysis, as behoves a student of G. H. Hardy. Much later, as he approached retirement, and for long after retirement, he produced very distinguished work on the history of mathematics. But there was very little publication in between; and I think that his entire published output on functional analysis consisted of just one substantial paper and two short notes.

**So what were the main ways in which Frank Smithies contributed to the development of the subject of “Functional Analysis’’ in Britain? **

I think that, in three ways, he had a very major influence:

- He was a great scholar of the subject – he read widely and kept himself up to date;
- He was a very effective lecturer on the subject;
- Above all, he was a prolific and conscientious supervisor of research students in the subject.

In all, he supervised more than 50 research students. Some of the early ones, myself included, benefited greatly when he pointed us in the direction of abstract problem, that arose naturally from his pre-war work. For a long time, he was the only functional analyst in the Cambridge Mathematics Department, supervising large numbers of research students. Around 1958, one of his former research students, John Williamson, joined him in Cambridge and relieved him of some, at least, of the work-load. By that time, there were quite lot of former Smithies research students, holding teaching posts and researching in functional analysis, dotted around various universities. These people made up a large proportion of the entire community of functional analysts in Britain, and some were by now supervising their own research students. At one point, a little later, the Newcastle mathematics department had five members of staff who had trained either as research students of Smithies, or as research students of former Smithies research students. The American mathematician, Paul Halmos, summed it up in describing Smithies as “the father (or grand father) of functional analysis in Great Britain’’.

**So what about the other Frank – Frank Bonsall?**

I believe that Frank Bonsall’s mathematical studies, as an undergraduate in Oxford, were interrupted by World War II. Certainly, his early career was put on hold, while he spent the war years in the army, mainly on the Indian subcontinent. Shortly thereafter, he was appointed to a junior teaching post in the mathematics department in Edinburgh. Although determined to be a researcher, he never had any formal training in research, was never a research student, and never took a PhD.

He first became interested in functional analysis when he heard (in his own words), “a brilliant lecture on commutative Banach algebras’’. This was at the British Mathematical Colloquium, in 1950, by Frank Smithies. After that, Bonsall’s emergence as a leading research worker in the subject was a tremendous achievement, largely the result of self-teaching, boosted by a year spent in the United States working with Nachman Aronszajn. He was attracted from Edinburgh to Newcastle, where the mathematics department had brilliant academic leadership from the classical analyst Werner Wolfgang Rogosinski. His research, mainly at that time on partially ordered vector spaces, flourished. With support from Rogosinski, he was able to build up the strongest research group, in the subject, in Britain at that time. As a member of that group in its later years, I learned a great deal from both Bonsall and Rogosinski. In 1965, Frank Bonsall returned, from Newcastle to Edinburgh, taking up a professorship, and beginning to build up a research group there.

**In the period, around 1966 or 1967, just before the formation of NBFAS, what were the main features of functional analysis in Britain?**

The main features of functional analysis in Britain at that time, could be summarised as follows:

- A strong research group developing in Edinburgh, with Frank Bonsall;
- A strong research group (including myself) in Newcastle, built up previously by Frank Bonsall, still developing;
- Frank Smithies and John Williamson in Cambridge, producing a lot of good research students;
- Quite a lot of individual researchers, many traceable back to Frank Smithies at first or second remove, dotted around various universities.

**When, where and how did the idea of establishing the NBFAS (North British Functional Analysis Seminar) arise and by whom?**

Around the time between 1966 and 1967, quite by accident, I met Frank Bonsall on a platform at King’s Cross railway station. We had each been to meetings in London that day (separate meetings) and were returning home – Newcastle for me, Edinburgh for Frank. So, from King’s Cross as far as Newcastle, we travelled together. A short while before that journey, the university of York had been through its procedures for appointing its first professor for pure mathematics, and I had been involved in that process as an external advisor to the university. As a result, although the appointment had not yet been announced publicly, I knew that John Williamson was about to leave Cambridge and become the new professor in York. Obviously, he would soon build up in York another research group in Functional Analysis – after all, in that period of rapid university expansion, there was always plenty of money sloshing around the system and permitting a few new appointments. So there would be research groups, in functional analysis, in York, in Newcastle and in Edinburgh. It had occurred to me that British Railways (as it was then) provided very easy travel between these three centres, along the east coast main line. I had concluded that this was a great opportunity for some fruitful inter – university collaboration. Clearly, something should be done.

On the journey from King’s Cross to Newcastle, I shared these ideas with Frank Bonsall. Perhaps unsurprisingly, he asked me for a bit more detail as to what I had in mind. That was a problem – I knew that something should be done, but I had not much clue as to what should be done. I think I waffled a bit, along the lines that surely three universities together could run a better seminar than any one could alone. When I left the train at Newcastle, we had agreed to give the matter further thought.

About a week later, I received a letter from Frank. It contained a blue-print – a model constitution, if you like – setting out how a number of universities could organise a joint seminar, in a way that would be beneficial to all and fair to each. It covered matters of objectives, governance, and administrative and financial arrangements. Also, in that letter, he suggested that it should be called

### “THE NORTH BRITISH FUNCTIONAL ANALYSIS SEMINAR’’

When we decided to go ahead with the project – probably just Newcastle and Edinburgh at first, because John Williamson was not yet established in York – I stepped back. In Newcastle, at that time, we had a young lecturer, who later became (in my view, at least) the best British functional analyst in the second half of the 20th century. I asked him to take care of Newcastle’s interest and participation in the new, joint seminar. So Barry Johnson became the first secretary of NBFAS, and had a major role in its early development. It grew to become more substantial and more successful than I could have imagined.

One final thought. For me, at least, the whole idea of an inter-university functional analysis seminar was prompted, in large measure, by the east coast main line through York, Newcastle and Edinburgh. The idea was discussed, for the first time and at length, during a journey along the east coast main line.

**Could you tell about your involvement and the roles you have held at the NBFAS after its establishment?**

After the formation of NBFAS, initially with just Edinburgh and Newcastle as members, I had no formal role in the organisation. In the early stages, I was able to get useful advice about administrative and financial arrangements for NBFAS, from the Finance Officer at Newcastle University (a man who was unfailingly helpful). I was never a member of the NBFAS committee. Of course, I attended and enjoyed the meetings, and from time to time suggested speakers.

The early decisions, as to just how the seminar could best operate, were taken by the NBFAS committee. I think that the main influence, initially, came from Frank Bonsall (in Edinburgh), with strong support (and a lot of hard work) from Barry Johnson (in Newcastle).

**How was your academic journey influenced by the NBFAS? If possible, could you support your answer by example(s) please? **

NBFAS was generally very successful in attracting speakers who were currently active in research and articulate in describing recent advances. So the lectures provided useful and interesting information on many aspects of functional analysis. But, for me at least, the most important feature of NBFAS was that it created a very supportive community of research workers in the subject. I think it helped many of us to retain enthusiasm for our research and optimism about further progress.

There was just one occasion when an NBFAS lecture provided specific information that was highly relevant to my own research at the time. The work I was doing then (in collaboration with R. V. Kadison) was on the cohomology of operator algebras, and our objectives seemed to require a programme involving several distinct steps. For some time, I had been aware that one of those steps could be reduced, in the abelian case, to the need to prove a rather attractive looking classical inequality. In my ignorance, I had never previously come across this inequality. Despite initially thinking that it should be a pretty simple matter to prove it, I had completely failed to do so. So it was quite a revelation to me when Joram Lindenstrauss, in a lecture on the geometry of Banach spaces, included an exposition of the well-known (but not to me!) Grothendieck Inequality!

This certainly set me working again, and did allow a proof (in the abelian case) of just one step in the programme. The non-commutative version of the Grothendieck Inequality (proved a few years later, I think by Gilles Pisier), would have given a proof of that one step in the general case.

Unfortunately, some of the other steps remained quite intractable, and the programme was never completed. Some of the cohomology questions, that Dick Kadison and I investigated, are (to the best of my knowledge) still open.

**How was the NBFAS supported (financially) at the time? **

NBFAS obtained its own funds through annual subscriptions from member universities. Each participating university could decide the extent of its commitment to (and, correspondingly, influence in) NBFAS by choosing how many “units’’ it held in the seminar. The subscription was pro-rata to the number of units.

At least in the case of Newcastle, the subscription had to be found from funds already available to the Mathematics Department (I imagine that much the same was true at other member universities). During the early days of NBFAS, the Newcastle mathematics department had quite a lot of research students, most of whom were supported by the Science Research Council (SRC). For each SRC supported research student, the department itself received an additional “Research Training Support Grant’’ (RTSG) to be used at its discretion for any research purposes. The Newcastle subscriptions to NBFAS were paid from the department’s RTSG income.

NBFAS used its own financial resources to cover its (rather small) administrative costs, and as a contingency fund to allow its activities to go ahead on the few occasions when other sources of support failed. Most NBFAS meetings were included as part of a wider programme (arranged by a member university in consultation with NBFAS) in which a research grant was obtained by that university to finance a visitor to that department, perhaps for a month or so. Generally, but not always, there grants came from SRC.

**What other activities did evolve from the NBFAS? **

I do not remember any NBFAS activities other than its meetings (usually just one day, but occasionally extending over two or three days), with lectures given by visiting academics.

**What other mathematical societies did exist at the early stages of (or even before) the establishment of the NBFAS?**

As far as I know, NBFAS was the first organisation set up in the UK with the specific purpose of organising inter-university seminars on Functional Analysis.

There were earlier organisations – the British Mathematical Colloquium (with an annual meeting covering pure mathematics as a whole) and an inter-university seminar on combinatorics which I think was organised largely by the Reading mathematics department. There were probably others. Later on, the North British Differential Equations Seminar was formed, modelled on NBFAS.