Abstract
Given Banach alebras \( \mathfrak{A}_1 \) and \( \mathfrak{A}_2 \) with maximal ideal spaces \( \mathcal{M}_1 \) and \( \mathcal{M}_2 \) , if \( \mathfrak{A}_1 \) and \( \mathfrak{A}_2 \) are isomorphic as algebras, then \( \mathcal{M}_1 \) and \( \mathcal{M}_2 \) are homeomorphic. It is thus to be expected that the topology of \( \mathcal{M}\left( \mathfrak{A} \right) \) is reflected in the algebraic structure of \( \mathfrak{A} \) , for an arbitrary Banach algebra \( \mathfrak{A} \) .
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© 1998 Springer-Verlag New York, Inc.
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(1998). The First Cohomology Group of a Maximal Ideal Space. In: Several Complex Variables and Banach Algebras. Graduate Texts in Mathematics, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22586-9_15
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DOI: https://doi.org/10.1007/978-0-387-22586-9_15
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98253-3
Online ISBN: 978-0-387-22586-9
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