Abstract
Spectral theory is developed in the setting of Banach algebras, and the Gelfand dual of a commutative Banach algebra is defined and studied. The Gelfand transform is studied for commutative C∗ algebras. The structure of the dual group in Pontryagin duality is shown for locally compact abelian groups
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Einsiedler, M., Ward, T. (2017). Banach Algebras and the Spectrum. In: Functional Analysis, Spectral Theory, and Applications. Graduate Texts in Mathematics, vol 276. Springer, Cham. https://doi.org/10.1007/978-3-319-58540-6_11
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DOI: https://doi.org/10.1007/978-3-319-58540-6_11
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-58539-0
Online ISBN: 978-3-319-58540-6
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