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Numerical ranges of the powers of an operator
Li, Chi-Kwong Choi, Man-Duen
Li, Chi-Kwong
Choi, Man-Duen
Abstract
The numerical range W(A) of a bounded linear operator A on a Hilbert space is the collection of complex numbers of the form (Av, v) with v ranging over the unit vectors in the Hilbert space. In terms of the location of W(A). inclusion regions are obtained for W(A(k)) for positive integers k, and also for negative integers k if A(-1) exists. Related inequalities on the numerical radius w(A) = sup{vertical bar u vertical bar: mu is an element of EW(A)} and the Crawford number c(A) = inf{vertical bar u vertical bar: mu is an element of W(A)} are deduced. (C) 2009 Elsevier Inc. All rights reserved.
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2010-01-01
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numerical_ranges.pdf
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Mathematics
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10.1016/j.jmaa.2009.10.066