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A factorable Banach algebra with inequivalent regular representation norm


Author: Michael Leinert
Journal: Proc. Amer. Math. Soc. 60 (1976), 161-162
MSC: Primary 46H99; Secondary 43A20
DOI: https://doi.org/10.1090/S0002-9939-1976-0420136-5
MathSciNet review: 0420136
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Abstract: An example is given of a semisimple commutative Banach algebra which factorizes but whose norm is not equivalent to the norm induced by its regular representation. This is a stronger version of the example given in [4] and it can be viewed as an example of a factorizing commutative abstract Segal algebra.


References [Enhancements On Off] (What's this?)

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  • [2] E. Hewitt and K. A. Ross, Abstract harmonic analysis. Vol. II, Grundlehren der math. Wiss., Band 152, Springer-Verlag, Berlin and New York, 1970. MR 41 #7378; erratum, 42, p. 1825. MR 551496 (81k:43001)
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  • [5] W. L. Paschke, A factorable Banach algebra without bounded approximate unit, Pacific J. Math. 46 (1973), 249-251. MR 47 #2765. MR 0324413 (48:2765)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0420136-5
Keywords: Banach algebra, factorization
Article copyright: © Copyright 1976 American Mathematical Society

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