On the algebra range of an operator on a Hilbert $C^*$-module over compact operators
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- by Rajna Rajić PDF
- Proc. Amer. Math. Soc. 131 (2003), 3043-3051 Request permission
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.References
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Additional Information
- Rajna Rajić
- Affiliation: Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia
- Email: rajna.rajic@zg.hinet.hr
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3043-3051
- MSC (2000): Primary 47A12, 46L08
- DOI: https://doi.org/10.1090/S0002-9939-03-07130-2
- MathSciNet review: 1993211