Quotient-bounded elements in locally convex algebras. II

Bhatt, Subhash J. (1985) Quotient-bounded elements in locally convex algebras. II Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 94 (2-3). pp. 71-91. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/94/2/71-91/...

Related URL: http://dx.doi.org/10.1007/BF02880988


Consideration of quotient-bounded elements in a locally convex GB*-algebra leads to the study of proper GB *-algebras viz those that admit nontrivial quotient-bounded elements. The construction and structure of such algebras are discussed. A representation theorem for a proper GB *-algebra representing it as an algebra of unbounded Hilbert space operators is obtained in a form that unifies the well-known Gelfand-Naimark representation theorem for C*-algebra and two other representation theorems for b*-algebras (also called LMC*-algebras), one representinga b *-algebra as an algebra of quotient bounded operators and the other as a weakly unbounded operator algebra. A number of examples are discussed to illustrate quotient-bounded operators. An algebra of unbounded operators constructed out of noncommutative L p-spaces on a regular probability gauge space and the convolution algebra of periodic distributions are analyzed in detail; whereas unbounded Hilbert algebras and Lw-integral of a measurable field of C*-algebras are discussed briefly.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Generalized B*-algebras; Unbounded Representations; Quotient-bounded Elements; Universally Bounded Elements; Unbounded Hilbert Algebras; Locally Multiplicative Convex (LMC) Algebras
ID Code:59682
Deposited On:07 Sep 2011 04:47
Last Modified:18 May 2016 10:09

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