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

Studia Mathematica (1993)

- Volume: 107, Issue: 3, page 273-286
- ISSN: 0039-3223

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topRusinek, Jan. "Pseudotopologies with applications to one-parameter groups, von Neumann algebras, and Lie algebra representations." Studia Mathematica 107.3 (1993): 273-286. <http://eudml.org/doc/216033>.

@article{Rusinek1993,

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.},

author = {Rusinek, Jan},

journal = {Studia Mathematica},

keywords = {pseudotopology; continuity; composition of operators; differentiability; one-parameter semigroup; von Neumann algebra; integration; Lie algebra representation; pseudotopological vector spaces; differentiability of certain operator- valued functions; strongly continuous one-parameter semigroups in Banach spaces; von Neumann algebras; integration of Lie algebra representations},

language = {eng},

number = {3},

pages = {273-286},

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

url = {http://eudml.org/doc/216033},

volume = {107},

year = {1993},

}

TY - JOUR

AU - Rusinek, Jan

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

JO - Studia Mathematica

PY - 1993

VL - 107

IS - 3

SP - 273

EP - 286

AB - 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.

LA - eng

KW - pseudotopology; continuity; composition of operators; differentiability; one-parameter semigroup; von Neumann algebra; integration; Lie algebra representation; pseudotopological vector spaces; differentiability of certain operator- valued functions; strongly continuous one-parameter semigroups in Banach spaces; von Neumann algebras; integration of Lie algebra representations

UR - http://eudml.org/doc/216033

ER -

## References

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- [T-W] J. Tits and L. Waelbroeck, The integration of a Lie algebra representation, Pacific J. Math. 26 (1968), 595-600. Zbl0172.18602

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