Numerical Ranges of the Powers of an Operator
نویسندگان
چکیده
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 (Ak) for positive integers k, and also for negative integers k if A−1 exists. Related inequalities on the numerical radius w(A) = sup{|μ| : μ ∈W (A)} and the Crawford number c(A) = inf{|μ| : μ ∈W (A)} are deduced. AMS Subject Classification 47A12, 47A50, 15A60.
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تاریخ انتشار 2009