The numerical range of an element of a normed algebra

Bonsall, F. F.

Glasgow mathematical journal, Tome 10 (1969) no. 1, pp. 68-72

Résumé

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 by

Détail

DOI : 10.1017/S0017089500000562

Bibliographie

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