By Sheldon Axler,Peter Rosenthal,Donald Sarason

Paul Richard Halmos, who lived a lifetime of unbounded devotion to arithmetic and to the mathematical neighborhood, died on the age of ninety on October 2, 2006. This quantity is a memorial to Paul by way of operator theorists he encouraged. Paul’sinitial research,beginning together with his 1938Ph.D. thesis on the collage of Illinois below Joseph Doob, was once in chance, ergodic concept, and degree concept. A shift happened within the Nineteen Fifties whilst Paul’s curiosity in foundations led him to invent a subject matter he termed algebraic common sense, leading to a succession of papers on that topic showing among 1954 and 1961, and the booklet Algebraic common sense, released in 1962. Paul’s ?rst papers in natural operator concept seemed in 1950. After 1960 Paul’s examine all for Hilbert area operators, a subject matter he seen as enc- passing ?nite-dimensional linear algebra. past his learn, Paul contributed to arithmetic and to its neighborhood in manifold methods: as a well known expositor, as an cutting edge instructor, as a tireless editor, and during unstinting carrier to the yankee Mathematical Society and to the Mathematical organization of the United States. a lot of Paul’s in?uence ?owed at a private point. Paul had a real, uncalculating curiosity in humans; he built a huge variety of friendships through the years, either with mathematicians and with nonmathematicians. a lot of his mathematical neighbors, together with the editors ofthisvolume,whileabsorbingabundantquantitiesofmathematicsatPaul’sknee, realized from his suggestion and his instance what it capacity to be a mathematician.

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A Glimpse at Hilbert Space Operators: Paul R. Halmos in Memoriam: 207 (Operator Theory: Advances and Applications) by Sheldon Axler,Peter Rosenthal,Donald Sarason

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