Existence of well-behaved *-representations of locally convex *-algebras

Bhatt, S. J. ; Fragoulopoulou, M. ; Inoue, A. (2006) Existence of well-behaved *-representations of locally convex *-algebras Mathematische Nachrichten, 279 (1-2). pp. 86-100. ISSN 0025-584X

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Official URL: http://onlinelibrary.wiley.com/doi/10.1002/mana.20...

Related URL: http://dx.doi.org/10.1002/mana.200310347

Abstract

The following problems are investigated: (1) The existence of well-behaved *-representations on a *-algebra A equipped with an unbounded m*-seminorm p, in terms of non-zero p-continuous representable (positive) linear functionals on the domain A(p) of p . (2) The existence of well-behaved *-representations of a locally convex *-algebra A, in terms of non-zero unbounded C *-seminorms on A with domain the *-subalgebra Ab generated by the hermitian part of the Allan bounded set A0 of A. (3) The existence of faithful well-behaved *-representations of a locally convex *-algebra A, in terms of the so-called unbounded Gel'fand-Naimark C *-seminorm on A.

Item Type:Article
Source:Copyright of this article belongs to John Wiley and Sons..
Keywords:Well-behaved *-representation;unbounded m- and C-seminorm;unbounded Gel'fand-Naimark C-Seminorm
ID Code:59685
Deposited On:07 Sep 2011 05:19
Last Modified:07 Sep 2011 05:19

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