Operator Algebras and C*-correspondences: A Survey

Kakariadis, Evgenios T. A.; Katsoulis, Elias G.

doi:10.1007/978-3-0348-0502-5_4

Cited by 4 publications

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“…One such application is contained in the recent paper of Davidson and the second author [6] regarding the C * -envelope of the universal operator algebra for the relations AX = X, where A, X are contractions. Other applications are currently being investigated by the authors in a sequel to the present paper [15].…”

Section: Introductionmentioning

confidence: 99%

Contributions to the theory of $\mathrm{C}^{*}$-correspondences with applications to multivariable dynamics

Kakariadis

Katsoulis

2012

Trans. Amer. Math. Soc.

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Motivated by the theory of tensor algebras and multivariable C *dynamics, we revisit two fundamental techniques in the theory of C *-correspondences, the "addition of a tail" to a non-injective C *-correspondence and the dilation of an injective C *-correspondence to an essential Hilbert bimodule. We provide a very broad scheme for "adding a tail" to a non-injective C *-correspondence; our scheme includes the "tail" of Muhly and Tomforde as a special case. We illustrate the diversity and necessity of our tails with several examples from the theory of multivariable C *-dynamics. We also exhibit a transparent picture for the dilation of an injective C *-correspondence to an essential Hilbert bimodule. As an application of our constructs, we prove two results in the theory of multivariable dynamics that extend earlier results. We also discuss the impact of our results on the description of the C *envelope of a tensor algebra as the Cuntz-Pimsner algebra of the associated C *-correspondence.

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Section: Introductionmentioning

confidence: 99%