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Full Description
This volume and its companion present a selection of the mathematical writings of P. R. Halmos. The present volume consists of research publications plus two papers which, although of a more expository nature, were deemed primarily of interest to the specialist ("Ten Problems in Hilbert Space" (1970d), and" Ten Years in Hilbert Space" (1979b)). The remaining expository and all the popular writings are in the second volume. The papers in the present volume are arranged chronologically. As it happens, that arrangement also groups the papers according to subject matter: those published before 1950 deal with probability and measure theory, those after 1950 with operator theory. A series of papers from the mid 1950's on algebraic logic is excluded; the papers were republished by Chelsea (New York) in 1962 under the title" Algebraic Logic." This volume contains two introductory essays, one by Nathaniel Friedman on Halmos's work in ergodic theory, one by Donald Sarason on Halmos's work in operator theory. There is an essay by Leonard Gillman on Halmos's expository and popular writings in the second volume. The editors wish to express their thanks to the staff of Springer-Verlag. They are grateful also for the help of the following people: C. Apostol, W. B. Arveson, R. G. Douglas, C. Pearcy, S. Popa, P. Rosenthal, A. L. Shields, D. Voiculescu, S. Walsh. Berkeley, CA Donald E. Sarason vii WORK IN OPERATOR THEORY P. R. Halmos's first papers on Hilbert space operators appeared in 1950.
Contents
[1939 a] Invariants of certain stochastic transformations: the mathematical theory of gambling systems.- [1942 d] On monothetic groups.- [1942 e] Operator methods in classical mechanics, II.- [1943] On automorphisms of compact groups.- [1944 a] Approximation theories for measure preserving transformations.- [1944 d] In general a measure preserving transformation is mixing.- [1947 c] Invariant measures.- [1949 b] Application of the Radon-Nikodym theorem to the theory of sufficient statistics.- [1950 a] Normal dilations and extensions of operators.- [1950 b] Commutativity and spectral properties of normal operators.- [1950 c] The marriage problem.- [1952 a] Spectra and spectral manifolds.- [1952 b] Commutators of operators.- [1953 a] Square roots of operators.- [1954 a] Commutators of operators, II.- [1958 b] Products of symmetries.- [1961 c] Shifts on Hilbert spaces.- [1963 c] Partial isometries.- [1963 d] Algebraic properties of Toeplitz operators.- [1964 a] Numerical ranges and normaldilations.- [1965 b] Cesàro operators.- [1966] Invariant subspaces of polynomially compact operators.- [1968 b] Irreducible operators.- [1968 c] Quasitriangular operators.- [1969 a] Invariant subspaces 1969.- [1969 b] Two subspaces.- [1970 d] Ten problems in Hilbert space.- [1971 a] Capacity in Banach algebras.- [1972 a] Continuous functions of Hermitian operators.- [1972 b] Positive approximants of operators.- [1972 c] Products of shifts.- [1973 b] Limits of shifts.- [1974 a] Spectral approximants of normal operators.- [1976 c] Some unsolved problems of unknown depth about operators on Hilbert space.- [1979 b] Ten years in Hilbert space.- [1980 a] Limsups of Lats.- [1982 d] Asymptotic Toeplitz operators.
