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Relations Between Generalized Growth Conditions and Several Classes of Convexoid Operators
Published online by Cambridge University Press: 20 November 2018
Extract
In this paper we shall discuss some classes of bounded linear operators on a complex Hilbert space. If T is a bounded linear operator T acting on the complex Hilbert space H, then the following two inequalities always hold:
where σ(T) indicates the spectrum of T, W(T) denotes the numerical range of T defined by W(T) = {(Tx, x) : ||x|| = 1 and x ∊ H} and means the closure of W(T) respectively.
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- Copyright © Canadian Mathematical Society 1977
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