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The numerical range of nonlinear Banach space operators. (English) Zbl 0796.47051
The author defines and studies a numerical range for nonlinear operators in Banach spaces which generalizes E. H. Zarantonello’s definition for Hilbert space operators [Pac. J. Math. 22, 575-595 (1967; Zbl 0152.346)]. It is shown, in particular, that the spectrum of a generalized Lipschitz operator is contained in the closed convex hull of its numerical range.

MSC:
47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)
47J05 Equations involving nonlinear operators (general)
Citations:
Zbl 0152.346
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References:
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[8] E. H. Zarantonello, The closure of the numerical range contains the spectrum,Pacific J. Math.,22 (1967), 575–595. · Zbl 0152.34602
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