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Noncommutative Variations on Theorems of Marcel Riesz and Others

In: PAUL HALMOS Celebrating 50 Years of Mathematics

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  • T. A. Gillespie

    (University of Edinburgh, Department of Mathematics)

Abstract

Paul Halmos spent part of a sabbatical year at Edinburgh University in 1973 at a time when operator theory was seeing some spectacular developments. The Brown-Douglas-Fillmore theory, bringing ideas from algebraic topology into operator theory, was rapidly coming to fruition; the Romanian school seemed to be solving important problems almost by the month; Lomonosov proved his celebrated invariant subspace theorem. The list could go on and on, but one common feature of many of these new results was that they were inspired by earlier work of Halmos and, in particular, were answering questions raised by him in his celebrated “Ten Problems ” paper [13]. All this meant that Halmos was very much at the information centre of things and we were caught up in the excitement of the times.

Suggested Citation

  • T. A. Gillespie, 1991. "Noncommutative Variations on Theorems of Marcel Riesz and Others," Springer Books, in: John H. Ewing & F. W. Gehring (ed.), PAUL HALMOS Celebrating 50 Years of Mathematics, pages 221-236, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0967-6_26
    DOI: 10.1007/978-1-4612-0967-6_26
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