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ArticleOriginal scientific text

Title

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

Authors 1

Affiliations

  1. Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Abstract

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.

Keywords

ENG
pseudotopology, continuity, composition of operators, differentiability, one-parameter semigroup, von Neumann algebra, integration, Lie algebra representation

Bibliography

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Studia Mathematica
1993/107/3
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Pages:
273-286
Main language of publication
English
Received
1993-01-10
Accepted
1993-05-27
Published
1993
Exact and natural sciences