By Sheldon Axler, Peter Rosenthal, Donald Sarason

The e-book is a commemorative quantity honoring the mathematician Paul R. Halmos (1916-2006), who contributed passionately to arithmetic in manifold methods, between them through simple learn, by means of exceptional mathematical exposition, through unselfish carrier to the mathematical group, and, no longer least, via the muse others present in his commitment to that community.Halmos made primary contributions in different parts of arithmetic. This quantity emphasises Halmos's contributions to operator idea, his venue for many of his mathematical lifestyles. The middle of the amount is a sequence of expository articles via favorite operator theorists supplying an summary of the way operator conception prospered in the course of the Halmos period, in no small degree because of Halmos's management and penetrating insights.

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On pure and applied Excerpt from: “Applied mathematics is bad mathematics”, pp. 9–20, appearing in Mathematics Tomorrow, edited by Lynn Steen, Springer-Verlag, New York (1981). It isn’t really (applied mathematics, that is, isn’t really bad mathematics), but it’s diﬀerent. Does that sound as if I had set out to capture your attention, and, having succeeded, decided forthwith to back down and become conciliatory? Nothing of the sort! The “conciliatory” sentence is controversial, believe it or not; lots of people argue, vehemently, that it (meaning applied mathematics) is not diﬀerent at all, it’s all the same as pure mathematics, and anybody who says otherwise is probably a reactionary establishmentarian and certainly wrong.

Halmos. Lectures on Boolean Algebras. Van Nostrand Mathematical Studies, no. 1, D. , Princeton, NJ, 1963. Paul R. Halmos. A Hilbert Space Problem Book. D. , Princeton–Toronto–London, 1967. Paul R. S. Sunder. Bounded Integral Operators on L2 Spaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, 96. Springer–Verlag, Berlin–New York, 1978. 40 Publications of Paul R. Halmos Paul R. Halmos. A Hilbert Space Problem Book. Second edition. Springer–Verlag, New York–Berlin, 1982. Paul R. Halmos. Selecta: Research Contributions.

1976-1) Products of involutions. Linear Algebra and Appl. H. Gustafson and H. Radjavi). (1976-2) American mathematics from 1940 to the day before yesterday. Amer. Math. H. H. H. H. P. Ziemer). (1976-3) Some unsolved problems of unknown depth about operators on Hilbert space. Proc. Royal Soc. Edinburgh Sect. A 76 (1976/77), 67–76. (1977-1) Logic from A to G. Math. Mag. 50 (1977), 5–11. (1977-2) The work of Frigyes Riesz (Hungarian). Mat. Lapok 29 (1977/81), 13–20. (1978-1) Integral operators. , Vol.