Abstract
Among Banach algebras there are very interesting ones called Banach algebras with involution. A mapping x → x⋆ from a Banach algebra A into itself is called an involution on A if it satisfies the following properties for all x,y ∈ A and λ ∈ ℂ:
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(i)
(x + y)⋆ = x⋆ + y⋆
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(ii)
\({{(\lambda x)}^{ \star }} = \bar{\lambda }{{x}^{ \star }},\)
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(iii)
(xy)⋆ = y⋆x⋆
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(iv)
(x⋆)⋆ = x.
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© 1991 Springer-Verlag New York, Inc.
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Aupetit, B. (1991). Representation Theory for C⋆-Algebras and the Spectral Theorem. In: A Primer on Spectral Theory. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3048-9_6
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DOI: https://doi.org/10.1007/978-1-4612-3048-9_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97390-6
Online ISBN: 978-1-4612-3048-9
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