Quotient-bounded elements in locally convex algebras. II

  • Subhash J Bhatt


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 noncommutativeL p-spaces on a regular probability gauge space and the convolution algebra of periodic distributions are analyzed in detail; whereas unbounded Hilbert algebras andL w-integral of a measurable field ofC *-algebras are discussed briefly.


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


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Copyright information

© Indian Academy of Sciences 1985

Authors and Affiliations

  • Subhash J Bhatt
    • 1
  1. 1.Department of MathematicsSardar Patel UniversityVallabhIndia

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