• Quotient-bounded elements in locally convex algebras. II

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    • Keywords


      Generalized B*-algebras; unbounded representations; quotient-bounded elements; universally bounded elements; unbounded Hilbert algebras; locally multiplicative convex (lmc) algebras

    • Abstract


      Consideration of quotient-bounded elements in a locally convexGB*-algebra leads to the study of properGB*-algebras viz those that admit nontrivial quotient-bounded elements. The construction and structure of such algebras are discussed. A representation theorem for a properGB*-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 forC*-algebra and two other representation theorems forb*-algebras (also calledlmc*-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 noncommutativeLp-spaces on a regular probability gauge space and the convolution algebra of periodic distributions are analyzed in detail; whereas unbounded Hilbert algebras andLw-integral of a measurable field ofC*-algebras are discussed briefly.

    • Author Affiliations


      Subhash J Bhatt1

      1. Department of Mathematics, Sardar Patel University, Vallabh, Vidyanagar - 388 120, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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