Bhatt, Subhash J. (1985) Quotientbounded elements in locally convex algebras. II Proceedings of the Indian Academy of Sciences  Mathematical Sciences, 94 (23). pp. 7191. ISSN 02534142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/94/2/7191/...
Related URL: http://dx.doi.org/10.1007/BF02880988
Abstract
Consideration of quotientbounded elements in a locally convex GB^{*}algebra leads to the study of proper GB ^{*}algebras viz those that admit nontrivial quotientbounded 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 wellknown GelfandNaimark 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 quotientbounded 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 L^{w}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; Quotientbounded 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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