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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The $ p$-class in a dual $ B\sp{\ast} $-algebra


Author: Pak Ken Wong
Journal: Trans. Amer. Math. Soc. 200 (1974), 355-368
MSC: Primary 46L05; Secondary 46K15
MathSciNet review: 0358371
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Abstract: In this paper, we introduce and study the class $ {A_p}(0 < p \leqslant \infty )$ in a dual $ {B^ \ast }$-algebra $ A$. We show that, for $ 1 \leqslant p \leqslant \infty ,{A_p}$ is a dual $ {A^ \ast }$-algebra which is a dense two-sided ideal of $ A$. If $ 1 < p < \infty $, we obtain that $ {A_p}$ is uniformly convex and hence reflexive. We also identify the conjugate space of $ {A_p}(1 \leqslant p < \infty )$. This is a generalization of the class $ {C_p}$ of compact operators on a Hilbert space.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0358371-X
PII: S 0002-9947(1974)0358371-X
Keywords: Dual $ {B^ \ast }$-algebra, hermitian minimal idempotent, uniform convexity, proper $ {H^ \ast }$-algebra
Article copyright: © Copyright 1974 American Mathematical Society