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Zeitschrift für Analysis und ihre Anwendungen

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Volume 21, Issue 1, 2002, pp. 203–208
DOI: 10.4171/ZAA/1072

Published online: 2002-03-31

Stably Solvable Maps are Unstable under Small Perturbations

Massimo Furi[1]

(1) Università di Firenze, Italy

We show that the set of stably solvable maps from an infinite dimensional Banach space $E$ into itself is not open in the topological space $C(E)$ of the continuous selfmaps of $E$. The question of whether or not this set is open is related to nonlinear spectral theory and was posed in [7].

Keywords: Nonlinear spectral theory, stably solvable maps, nonlinear operators

Furi Massimo: Stably Solvable Maps are Unstable under Small Perturbations. Z. Anal. Anwend. 21 (2002), 203-208. doi: 10.4171/ZAA/1072