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

Tom 107 / 1993

Jan Rusinek Studia Mathematica 107 (1993), 273-286 DOI: 10.4064/sm-107-3-273-286

Streszczenie

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.

Autorzy

  • Jan Rusinek

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