Pseudotopologies with applications to one-parameter groups, von Neumann algebras, and Lie algebra representations
Rusinek, Jan
Studia Mathematica, Tome 104 (1993), p. 273-286 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:216033 
@article{bwmeta1.element.bwnjournal-article-smv107i3p273bwm,
     author = {Jan Rusinek},
     title = {Pseudotopologies with applications to one-parameter groups, von Neumann algebras, and Lie algebra representations},
     journal = {Studia Mathematica},
     volume = {104},
     year = {1993},
     pages = {273-286},
     zbl = {0810.46005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv107i3p273bwm}
}

Rusinek, Jan. Pseudotopologies with applications to one-parameter groups, von Neumann algebras, and Lie algebra representations. Studia Mathematica, Tome 104 (1993) pp. 273-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv107i3p273bwm/

[00000] [B] A. Bastiani, Applications différentiables et variétés différentiables de dimension infinie, J. Anal. Math. 13 (1964), 1-114. | Zbl 0196.44103

[00001] [B-R] O. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics, Springer, New York, 1979.

[00002] [D] E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980. | Zbl 0457.47030

[00003] [F-B] A. Frölicher and W. Bucher, Calculus in Vector Spaces without Norm, Lecture Notes in Math. 30, Springer, New York, 1966. | Zbl 0156.38303

[00004] [J-M] P. E. T. Jørgensen and T. Moore, Operator Commutation Relations, Reidel, Dordrecht, 1984.

[00005] [Ke] H. H. Keller, Differenzierbarkeit in topologischen Vektorräumen, Comment. Math. Helv. 38 (1964), 308-320. | Zbl 0124.06402

[00006] [K] J. Kisyński, On the integration of a Lie algebra representation in a Banach space, internal report, International Centre for Theoretical Physics, Triest, 1974.

[00007] [R] J. Rusinek, Analytic vectors and integrability of Lie algebra representations, J. Funct. Anal. 74 (1987), 10-23. | Zbl 0643.22007

[00008] [T-W] J. Tits and L. Waelbroeck, The integration of a Lie algebra representation, Pacific J. Math. 26 (1968), 595-600. | Zbl 0172.18602