On the numerical range of an operator
1963; American Mathematical Society; Volume: 14; Issue: 1 Linguagem: Inglês
10.1090/s0002-9939-1963-0143035-6
ISSN1088-6826
Autores Tópico(s)Algebraic and Geometric Analysis
ResumoThe numerical range of an operator P in a Hubert space is defined as the set of all the complex numbers (Tx, x), where x is a unit vector in the space.It is well known that a bounded normal operator has the property that the closure of its numerical range is exactly the convex hull of its spectrum [5, Theorem 8.13 and Theorem 8.14].Call this property A. In this article let P denote a linear bounded operator in a Hilbert space H, V(T) be its numerical range, K(T) be the convex hull of its spectrum, and use the usual notations p(T), <t(T), Pa(T), Ca(T), Rcr(T) respectively for the resolvent set, spectrum, point spectrum, continuous spectrum,and residual spectrum of P.This article shall investigate some consequences of the property
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