Functional calculus and ∗-regularity of a class of Banach algebras II
✍ Scribed by Chi-Wai Leung; Chi-Keung Ng
- Book ID
- 108175385
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 167 KB
- Volume
- 322
- Category
- Article
- ISSN
- 0022-247X
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📜 SIMILAR VOLUMES
The symbolic calculus on Banach algebras of continuous functions and related spaces is studied. In particular, functions operating on the real part of the algebra are considered. The main tool in this paper is an ultraseparation argument. As a consequence it is shown, for example, that \(t^{p}\) on
We show among other things that if B is a Banach function space of continuous real-valued functions vanishing at infinity on a locally compact Hausdorff space X, with the property that for some odd natural number p>1, b 1Â p # B for all b # B, then B=C 0 (X ).
## Abstract The presence of a modulus function on a Banach algebra gives rise to tensor product norms analogous to the greatest cross‐norm and allows us to extend the Waelbroeck functional calculus. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)