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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the algebra range of an operator on a Hilbert $C^*$-module over compact operators


Author: Rajna Rajic
Journal: Proc. Amer. Math. Soc. 131 (2003), 3043-3051
MSC (2000): Primary 47A12, 46L08
Published electronically: May 5, 2003
MathSciNet review: 1993211
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Abstract: Let $X$ be a Hilbert $C^*$-module over the $C^*$-algebra $K(H)$ of all compact operators on a complex Hilbert space $H$. Given an orthogonal projection $p \in K(H)$, we describe the set $ V^n(A) = \{\langle Ax,x\rangle \,\,:\,\,x\in X,\,\,\langle x,x \rangle =p\} $ for an arbitrary adjointable operator $A\in B(X)$. The relationship between the set $ V^n(A)$ and the matricial range of $A$ is established.


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Additional Information

Rajna Rajic
Affiliation: Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia
Email: rajna.rajic@zg.hinet.hr

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07130-2
PII: S 0002-9939(03)07130-2
Keywords: $C^*$-algebra, Hilbert $C^*$-module, adjointable operator, matricial range of an operator
Received by editor(s): June 20, 2001
Received by editor(s) in revised form: January 22, 2002
Published electronically: May 5, 2003
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society