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Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 12 (2017), 7 -- 21

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This work is licensed under a Creative Commons Attribution 4.0 International License.


M. Kian and M. Dehghani

Abstract. Let A and B be C*-algebras. We consider a noncommutative convexity in Hilbert A-B-bimodules, called A-B-convexity, as a generalization of C*-convexity in C*-algebras. We show that if X is a Hilbert A-B-bimodule, then Mn(X) is a Hilbert Mn(A)-Mn(B)-bimodule and apply it to show that the closed unit ball of every Hilbert A-B-bimodule is A-B-convex. Some properties of this kind of convexity and various examples have been given.

2010 Mathematics Subject Classification: Primary 46L89; Secondary 52A01, 46L08.
Keywords: Matrix convex set; C*-algebra; Hilbert C*-bimodule; noncommutative convexity.

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Mohsen Kian
Department of Mathematics,
Faculty of Basic Sciences,
University of Bojnord,
P. O. Box 1339, Bojnord 94531, Iran.
School of Mathematics,
Institute for Research in Fundamental Sciences (IPM),
P.O. Box: 19395-5746, Tehran, Iran.
email: kian@ub.ac.ir  and  kian@member.ams.org

Mahdi Dehghani (Corresponding author)
Department of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Kashan,
P. O. Box 87317-53153, Kashan, Iran.
email: m.dehghani@kashanu.ac.ir