Geodesic
Pseudotopologies with applications to one-parameter groups, von Neumann algebras, and Lie algebra representations
Studia Mathematica, Tome 107 (1993) no. 3, pp. 273-286

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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.
DOI : 10.4064/sm-107-3-273-286
Keywords: pseudotopology, continuity, composition of operators, differentiability, one-parameter semigroup, von Neumann algebra, integration, Lie algebra representation

Jan Rusinek 1

1 
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Jan Rusinek. Pseudotopologies with applications to one-parameter groups, von Neumann algebras, and Lie algebra representations. Studia Mathematica, Tome 107 (1993) no. 3, pp. 273-286. doi: 10.4064/sm-107-3-273-286

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