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arXiv · 1703.10063

Operator *-correspondences in analysis and geometry

David Blecher·Jens Kaad·Bram Mesland
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Abstract

An operator *-algebra is a non-selfadjoint operator algebra with completely isometric involution. We show that any operator *-algebra admits a faithful representation on a Hilbert space in such a way that the involution coincides with the operator adjoint up to conjugation by a symmetry. We introduce operator *-correspondences as a general class of inner product modules over operator *-algebras and prove a similar representation theorem for them. From this we derive the existence of linking operator *-algebras for operator *-correspondences. We illustrate the relevance of this class of inner product modules by providing numerous examples arising from noncommutative geometry.

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David Blecher, Jens Kaad, Bram Mesland. 2017-03-29. Operator *-correspondences in analysis and geometry. https://doi.org/10.1112/plms.12129

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