A note on the shape of the generalized numerical range
- 1 January 1990
- journal article
- research article
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 26 (1-2) , 43-47
- https://doi.org/10.1080/03081089008817964
Abstract
Let c = c 1,…,c k εCk and let T: be a bounded linear operator on a complex Hilbert space The set Wc (T) of all numbers of the form obtained by letting (e 1,…,e k) vary over all k-tuples of orthonomal vectors in is called the c numerical range of T. In recent years, several results about the c-numerical ranges of operators on finite-dimensional Hilbert spaces have been published. The purpose of this note is to prove two theorems concerning c-numerical reanges in the infinite-dimensional case. By obtaining a converse to a theorem due to Westwick. We characterize those k-tuples for which Wc (T) is convex for all We show also that the closure of Wc (T) is star-shapted with respect to each point in where We (T) denotes the essential numerical range of T.Keywords
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