Extensions of -representations

Author:
Andreas Kasparek

Journal:
Proc. Amer. Math. Soc. **109** (1990), 1069-1077

MSC:
Primary 46K10; Secondary 47D40

DOI:
https://doi.org/10.1090/S0002-9939-1990-1012932-8

MathSciNet review:
1012932

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Abstract: Let be a -representation of a -algebra . In general the strong commutant and Theory weak commutant of the -algebra do not coincide. We are looking for some methods to get extensions of such that the related commutants coincide or which are even selfadjoint. In §§2 and 3 we consider so-called generated extensions that are a modification of induced extensions investigated by Borchers, Yngvason [1] and Schmüdgen [7]. In §4 let be a -algebra and a subset of its hermitian part such that is generated by as an algebra. We present a method to extend -representations of such algebras, which is closely related with the extension of the symmetric operators . In §5 we give an example that shows that the method of generated extensions is also suitable to get extensions such that the commutants of the related -algebras coincide.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1012932-8

Keywords:
Extensions of -representations,
commutants of -algebras

Article copyright:
© Copyright 1990
American Mathematical Society