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Some Results on the Center of an Algebra of Operators on VN(G) for the Heisenberg group

Published online by Cambridge University Press:  20 November 2018

C. Cecchini  and
A. Zappa
C. Cecchini
Affiliation:
Universitá di Genova, Genova, Italy
A. Zappa
Affiliation:
Universitá di Genova, Genova, Italy
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Let G be an amenable locally compact group. We will use the terminology of [3] and denote by VN(G) the Von Neumann algebra of the regular representation and by A(G) its predual, which is the algebra of the coefficients of the regular representation. The Von Neumann algebra VN(G) is, in a natural fashion, a module with respect to A(G) [3].

The algebra of bounded linear operators on VN(G), which commute with the action of A(G), has been studied in [6] and in [1]. If UCB(Ĝ) is the space of the elements of VN(G) of the form vT, for some v in A(G) and some T in VN(G) (see for instance [4]), in [6] and in [1] it is proved that, for any amenable locally compact group there exists an isometric bijection between and UCB(Ĝ)*.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 6 , 01 December 1981 , pp. 1469 - 1486
Copyright
Copyright © Canadian Mathematical Society 1981

References

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