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.


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)


Zbl 0152.346
Full Text: DOI


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