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arXiv · 1409.1329

Spectral Theory on Commutative Krein C*-algebras

Pichkitti Bannangkoon·Paolo Bertozzini·Wicharn Lewkeeratiyutkul
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Abstract

A Banach involutive algebra is called a Krein C*-algebra if there is a fundamental symmetry (an involutive automorphism of period 2) such that the C*-property is satisfied when the original involution is replaced with the new one obtained by composing the automorphism with the old involution. For a given fundamental symmetry, a Krein C*-algebra decomposes as a direct sum of an even part (a C*-algebra) and an odd part (a Hilbert C*-bimodule on the even part). Our goal here is to develop a spectral theory for commutative unital Krein C*-algebras when the odd part is a symmetric imprimitivity C*-bimodule over the even part and there exists an additional suitable "exchange symmetry" between the odd and even parts.

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Pichkitti Bannangkoon, Paolo Bertozzini, Wicharn Lewkeeratiyutkul. 2014-09-04. Spectral Theory on Commutative Krein C*-algebras. https://arxiv.org/abs/1409.1329

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