orthogonality — 1 articles found.

A remark on orthogonality of elements of a C*-algebra

C. R. Math. Rep. Acad. Sci. Canada Vol. 31 (3) 2009, pp. 72–75
Vol.31 (3) 2009
George A. Elliott Details
(Received: 2008-12-27 )
(Received: 2008-12-27 )

George A. Elliott, Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 2E4; e-mail: elliott@math.toronto.edu

Abstract/Résumé:

A remark on orthogonality of elements of a C*-algebra Resume/Abstract: It is shown that any two non-zero hereditary sub-C*-algebras of a C*-algebra that has no minimal projections have approximately orthogonal elements of norm one. (The question of exact orthogonality is left open.)

On démontre que, dans une C*-algèbre sans projecteur minimal, deux sous-C*-algèbres héréditaires qui ne sont pas égales à zéro possèdent des éléments de norme un qui sont approximativement orthogonals.

Keywords: C*-algebra, approximate orthogonality, hereditary subalgebras, orthogonality

AMS Subject Classification: General theory of $C^*$-algebras 46L05

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