The numerical range of an element of a normed algebra
- 1 January 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal
- Vol. 10 (1) , 68-72
- https://doi.org/10.1017/s0017089500000562
Abstract
Given a normed linear space X, let S(X), X′, B(X) denote respectively the unit sphere {x: ∥x∥ = 1} of X, the dual space of X, and the algebra of all bounded linear mappings of X into X. For each x ∊ S(X) and T ∊ B(X), let Dx(x) = {f e X′:∥f∥ = f(x)= 1}, and V(T; x) = {f(Tx):f∊Dx(x)}. The numerical range V(T) is then defined byKeywords
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