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Professor Richard Timoney of Trinity College Dublin, in his contribution to the book "Trevor West: The Bold Collegian" (author Maura Lee West) about the multi-talented Trevor West, wrote the following remembrance of Gerard: Among the students he (Trevor) had, some were deserving of his particular interest ever after. One of those was Gerard Murphy (1948 - 2006) who was not a Ph.D. student of Trevor’s but had a close relationship with him. Gerard came from a working class background in Dublin and missed out on a normal secondary education, but came to the notice of the School of Mathematics in Trinity. Trevor took a special interest in him, and was pleased that Gerard turned out as a very good undergraduate in Mathematics. Gerard did his doctorate at Cambridge, not with Trevor's supervisor Smithies but with one of Smithies' mathematical descendants, finishing in 1977. Then he got a postdoctoral fellowship back at Trinity, where he worked productively with Trevor. Following three years at TCD, Gerard held some positions in North America before being appointed in Cork, where he was again within close reach of Trevor from the West family home in Midleton. Trevor encouraged Gerard to organise international research meetings in Cork, of which there were quite a few, and Trevor was always in the thick of them.

Among the several joint papers between Murphy and West, Finbarr Holland picks out a spectral radius formula for special mention in an obituary of Gerard that appeared in the Bulletin of the Irish Mathematical Society (no. 59, 2007). It is a particularly elegant formula for the spectral radius of an element in a C*-algebra that was published in a paper in the Proceedings of the Edinburgh Mathematical Society in 1979. One should also mention that Gerard was elected to membership of the RIA and became editor of the Mathematical Proceedings, both of which events were surely engineered by Trevor. As with many things, Trevor would not miss opportunities to plug his favourites and the considerable merits of Gerard were easy to extol, but of course Gerard’s terminal illness was a blow. Maybe the most notable joint effort between them was Trevor’s second mathematical monograph, often referred to as ‘the little red book’, which was in fact a joint effort between four authors, Bruce Barnes of Oregon, Gerard Murphy, Roger Smyth (former doctoral student) and Trevor. The book appeared in 1982 and has a lasting value that is really noteworthy. It is not so much that the overall thrust of the book is still current, but rather that there are defnitions and lemmas in it that remain useful and are not available elsewhere.

Roger Smyth was the first of Trevor’s two Ph.D. students and Trevor always spoke enthusiastically about their work together, which spanned many years. Roger was employed as a civil servant in the Northern Ireland Department of Health and Social Services, and so did his Mathematics outside of his working hours. Apart from the fact that Trevor got on very well with Roger, it suited Trevor to have Roger among his Northern Ireland friends and informants on political matters. In a different way, Alastair Gillespie was well placed in Edinburgh where there were rugby matches to attend every now and again, while the Cork connection with Gerard was a different kind of overlap of interests. By the way, the collaboration with Rien Kaashoek did not seem to have any similar coincidence but they did travel often between Dublin and Amsterdam to collaborate. Rainer Nagel of Tubingen was also a close contact of Trevor’s but not a co-author.

With regard to the red book, actually entitled Riesz and Fredholm Theory in Banach Algebras and published by Pitman in 1982, Roger Smyth credits Trevor with being the mastermind and driving force behind the book. For instance, Trevor would have been the host for Bruce Barnes during his sabbatical year in Trinity (1979- 0) and Roger also recalls Trevor deciding rather late on that a significant section of the book was not written in the ‘right way’ and coming up with a new and clearer approach during the final stages of preparation. It seems Trevor also did the management work such as dealing with the publisher and managing the production of the camera- ready copy (in those days using a typist with a golf ball typewriter). Roger’s influence on the book is quite clearly related to his doctoral work and subsequent work with Trevor, Bruce Barnes’ research at the time was also close to the topics discussed and perhaps Gerard was more interested in the parts where C*-algebras enter. It is appropriate to quote the last paragraph from the Mathematical Review of the book:

‘The aim of the authors is “to highlight the interplay between algebra and spectral theory which emerges in any penetrating analysis of compact, Riesz and Fredholm operators on Banach spaces”. Their little book proves, among other things, that they have fully (and beautifully) achieved this aim.’

Possibly an important contribution from Gerard Murphy to the book, or maybe something he picked up while engaged in it, was a facility for explaining things particularly well. Later, in 1990, Gerard published a book called C*-algebras and operator theory (Academic Press) which has remained a standard reference. It covers the basics of the theory but also dips in to the more advanced and modern aspects in such a way that many new students of C*-algebras continue to fnd it a valuable introduction, preferable for the beginner to many fatter and more encyclopedic volumes. https://en.wikipedia.org/wiki/Trevor_West This remembrance was added by Carol Murphy, Gerard's sister 12 October 2017 with kind permission of Dr Timoney and Maura Lee West (author) The Bold Collegian.