Bounded vectors for unbounded representations and standard representations of polynomial algebras

Bhatt, Subhash J. (1993) Bounded vectors for unbounded representations and standard representations of polynomial algebras The Yokohama mathematical journal, 41 (1). pp. 67-83. ISSN 0044-0523

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Abstract

Let A be a unital commutative *-algebra. Let π be a hermitian representation of A into (not necessarily bounded) Hilbert space operators. Analytic vectors and bounded vectors for π are investigated; and are used to show that π is a direct sum of bounded (operator) representations iff π admits a core consisting of bounded vectors. This, in turn, is used to show that if A is either of the polynomial algebras ζ(x) or ζ(x, y) in one or two commuting hermitian generators then π is standard iff π is a direct sum of bounded representations. Various selfadjointness and standardness criteria for representations of these polynomial algebras are developed, highlighting the difference between the representation theory of these two algebras, and supplementing known results.

Item Type:Article
Source:Copyright of this article belongs to Yokohama National University.
ID Code:59701
Deposited On:07 Sep 2011 05:15
Last Modified:18 May 2016 10:10

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