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2016 | OriginalPaper | Chapter

3. Banach Algebras and C ∗-Algebras

Authors : H. G. Dales, F. K. Dashiell Jr., A. T.-M. Lau, D. Strauss

Published in: Banach Spaces of Continuous Functions as Dual Spaces

Publisher: Springer International Publishing

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Abstract

This chapter will first give the basic background that we shall require concerning Banach algebras, C ∗-algebras, and von Neumann algebras. In particular, in \(\S\) 3.1, we shall discuss the bidual of a Banach algebra, taken with its Arens products. In \(\S\) 3.3, we shall exhibit the Baire classes as examples of commutative C ∗-algebras. We shall conclude the chapter in \(\S\) 3.4 with a few remarks on the generalizations of some of our discussions concerning the commutative C ∗-algebras C  0(K) to general (non-commutative) C ∗-algebras; as we said, these generalizations will not be used within our main text.

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previous chapter Banach Spaces and Banach Lattices
next chapter Measures
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Metadata
Title
Banach Algebras and C ∗-Algebras
Authors
H. G. Dales
F. K. Dashiell Jr.
A. T.-M. Lau
D. Strauss
Copyright Year
2016
Book
Banach Spaces of Continuous Functions as Dual Spaces

Print ISBN: 978-3-319-32347-3

Electronic ISBN: 978-3-319-32349-7

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-32349-7_3

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