Abstract
For most of the mathematical public the name Paul Halmos is synonymous with excellent mathematical exposition. Having been Paul’s colleague for many years, both as a faculty member at Indiana University and as a researcher in operator theory, I feel that I know many other aspects of his mathematical personality. To begin with, he is totally dedicated to mathematics and scholarship. He works harder than most mathematicians I know. His reputation as a lecturer is results in careful preparation and great attention to detail.
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References
C. Apostol, L. Fialkow, D. Herrero, and D. Voiculescu, Approximation of Hilbert Space Operators, Pitman Publishing Co., London, 1984.
C. Apostol, C. Foias, and D. Voiculescu, “Some results on non-quasi-triangulax operators, IV,”Rev. Roumaine Math. Pures Appl. 18 (1973), 487–514.
C. Apostol, D.A. Herrero, and D. Voiculescu, “The closure of the similarity orbit of a Hilbert space operator,” Bull. Am. Math. Soc. 6 (1982), 421–426.
C. Apostol and B.B. Morrel, “On uniform approximation of operators by simple models,” Indiana Univ. Math. J. 26 (1977), 427–442.
C. Apostol and D. Voiculescu, “On a problem of Halmos,” Rev. Roumaine Math. Pures Appl. 19 (1974), 283–284.
N. Aronszajn and K.T. Smith, “Invariant subspaces of completely continuous operators,” Ann. Math. 60 (1954), 345–350.
J. Bram, “Subnormal operators,” Duke Math. J. 22 (1955), 75–94.
J.B. Conway, A Course in Functional Analysis, Second edition, Springer-Verlag, New York, 1990.
J.B. Conway, The Theory of Subnormal Operators, Amer. Math. Soc. Math. Surveys, Vol. 36, Providence, 1991.
R.G. Douglas and C. Pearcy, “A note on quasitriangular operators,” Duke Math. J. 37 (1970), 177–188.
R.G. Douglas and C. Pearcy, “Invariant subspaces of non-quasitriangular operators,” Proc. Conf. Operator Theory, Springer Lectures Notes, Springer-Verlag, Berlin, 1973, Vol. 345.
P.R. Halmos, “Normal dilations and extensions of operators,” Summa Bras. Math. 2 (1950), 125–134.
P.R. Halmos, “Quasitriangular operators,” Acta Sci. Math. (Szeged) 29 (1968), 283–293.
P.R. Halmos, “Irreducible operators,” Michigan Math. J. 15 (1968), 215–233.
P.R. Halmos, “Ten problems in Hilbert space,” Bull. Am. Math. Soc. 76 (1970), 887–933.
P.R. Halmos, “Positive approximants of operators,” Indiana Math. J. 21 (1972), 951–960.
P.R. Halmos, “Ten years in Hilbert space,” Integral Equations Operator Theory 2 (1979), 529–564.
D.A. Herrero, Approximation of Hilbert Space Operators, I, Pitman Publishing Co., London, 1982.
M. Martin and M. Putinar, Lectures on Hyponormal Operators, Birkhäuser, Basel, 1982.
B. Sz-Nagy, “Sur les contractions de l’espace de Hilbert,” Acta Sci. Math. (Szeged) 15 (1953), 87–52.
B. Sz-Nagy and C. Foias, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970.
D. Voiculescu, “Norm-limits of algebraic operators,” Rev. Roumaine Math. Pures Appl. 19 (1974), 371–378.
D. Voiculescu, “A non-commutative Weyl-von Neumann Theorem,” Rev. Roumaine Math. Pures Appl. 21 (1976), 97–113.
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Conway, J.B. (1991). Paul Halmos and the Progress of Operator Theory. In: Ewing, J.H., Gehring, F.W. (eds) PAUL HALMOS Celebrating 50 Years of Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0967-6_20
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DOI: https://doi.org/10.1007/978-1-4612-0967-6_20
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