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Journal of Operator Theory

Volume 87, Issue 1, Winter 2022  pp. 229-248.

Completely bounded subcontexts of a Morita context of unital $C^*$-algebras

Authors:  Kathryn McCormick
Author institution: Department of Mathematics and Statistics, California State University Long Beach, 1250 Bellflower Boulevard, Long Beach, 90840, U.S.A.

Summary: We answer a question of Blecher--Muhly--Paulsen, identifying topological invariants for cb Morita equivalences of holomorphic cross-section algebras. Previously, given a certain subcontext of a Morita context of $n$-homogeneous $C^*$-algebras whose spectrum $T$ is an annulus, the norm of a lifting of $1_\mathcal{A}$ of a given subalgebra $\mathcal{A}$ was estimated by conformal and bundle invariants. We give a generalization in which $T$ is a bordered Riemann surface. In doing so, we develop a sufficient criterion for when a unital completely bounded Morita equivalence can be factored into a similarity and a strong Morita equivalence.

Keywords: operator algebra, nonselfadjoint, homogeneous $C^*$-algebra, Morita context, Morita equivalence, Riemann surface, matrix bundle

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