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The p-classes of an H∗-algebra
James F. Smith |
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Vol. 42 (1972), No. 3, 777–793
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Abstract |
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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
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Milestones
Received: 23 July 1971
Revised: 23 November 1971
Published: 1 September 1972
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Authors |
| James F. Smith | |
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