Vol. 42, No. 3, 1972

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The p-classes of an H∗-algebra

James F. Smith

Vol. 42 (1972), No. 3, 777–793
Abstract

This paper considers a family of -subalgebras of a semisimple H-algebra A. For 0 < p a nonnegative extendedreal value |a|p is associated with each a in A; then the p-class Ap is defined to be {a A : |a|p < ∞}. If 1 p ,Ap is then a two-sided -ideal of A (proper only if p < 2), and (Ap,|⋅|p) is a normed -algebra. (A2,|⋅|2) is (A,∥⋅∥); and for 1 p < 2,(Ap,|⋅|p) is a Banach -algebra, for which structure theorems are given.

Mathematical Subject Classification 2000
Primary: 46K15
Milestones
Received: 23 July 1971
Revised: 23 November 1971
Published: 1 September 1972
Authors
James F. Smith