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1993 | 107 | 3 | 273-286
Tytuł artykułu

Pseudotopologies with applications to one-parameter groups, von Neumann algebras, and Lie algebra representations

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EN
Abstrakty
EN
For any pair E,F of pseudotopological vector spaces, we endow the space L(E,F) of all continuous linear operators from E into F with a pseudotopology such that, if G is a pseudotopological space, then the mapping L(E,F) × L(F,G) ∋ (f,g) → gf ∈ L(E,G) is continuous. We use this pseudotopology to establish a result about differentiability of certain operator-valued functions related with strongly continuous one-parameter semigroups in Banach spaces, to characterize von Neumann algebras, and to establish a result about integration of Lie algebra representations.
Twórcy
autor
  • Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland, rusinek@mimuw.edu.pl
Bibliografia
  • [B] A. Bastiani, Applications différentiables et variétés différentiables de dimension infinie, J. Anal. Math. 13 (1964), 1-114.
  • [B-R] O. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics, Springer, New York, 1979.
  • [D] E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980.
  • [F-B] A. Frölicher and W. Bucher, Calculus in Vector Spaces without Norm, Lecture Notes in Math. 30, Springer, New York, 1966.
  • [J-M] P. E. T. Jørgensen and T. Moore, Operator Commutation Relations, Reidel, Dordrecht, 1984.
  • [Ke] H. H. Keller, Differenzierbarkeit in topologischen Vektorräumen, Comment. Math. Helv. 38 (1964), 308-320.
  • [K] J. Kisyński, On the integration of a Lie algebra representation in a Banach space, internal report, International Centre for Theoretical Physics, Triest, 1974.
  • [R] J. Rusinek, Analytic vectors and integrability of Lie algebra representations, J. Funct. Anal. 74 (1987), 10-23.
  • [T-W] J. Tits and L. Waelbroeck, The integration of a Lie algebra representation, Pacific J. Math. 26 (1968), 595-600.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv107i3p273bwm
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