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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Dual $ A\sp{\ast} $-algebras of the first kind


Authors: David L. Johnson and Charles D. Lahr
Journal: Proc. Amer. Math. Soc. 74 (1979), 311-314
MSC: Primary 46H05; Secondary 46K15, 46L05
MathSciNet review: 524307
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Abstract: Let A be an $ {A^\ast}$-algebra of the first kind. It is proved that A has property P2 of Máté if and only if $ {A^2}$ is dense in A if and only if A possesses an (operator-bounded) approximate identity. Further, it is shown that an $ {A^\ast}$-algebra of the first kind having property P2 is a dual algebra if and only if it is a modular annihilator algebra. As applications, these results are used to strengthen certain theorems about Hilbert algebras.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0524307-1
PII: S 0002-9939(1979)0524307-1
Keywords: Approximate identity, multiplier, $ {A^\ast}$-algebra, dual algebra, modular annihilator algebra, Hilbert algebra
Article copyright: © Copyright 1979 American Mathematical Society