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An Infinite Dimensional 0-epi Mapping with Degree Zero

✍ Scribed by Zouhua Ding

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
135 KB
Volume
199
Category
Article
ISSN
0022-247X

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✦ Synopsis

Let X be a real Banach space and let D ; X be an open and bounded set. A Ε½ . mapping T : D Βͺ X with 0 f T Ρ¨ D is called 0-epi mapping on D if the equation Ε½ . Tx s g x is solvable in D for every compact continuous mapping g: D Βͺ X which vanishes identically on Ρ¨ D. We show that there exists a mapping T : 2 2 Ε½ l> D Βͺ l such that the mapping I y T is 0-epi, but the degree deg I y T y g, . D, 0 is well defined and equals zero, for any such function g. This says that the degree theory cannot be applied directly to I y T y g in order to guarantee the Ε½ . Ε½ . solvability of I y T x s g x in D for any mapping g as above. This fact provides a good justification for the study of 0-epi mappings by M. Furi, M. Martelli, and A.

Ε½ .

πŸ“œ SIMILAR VOLUMES

A Characterization of 0-epi Maps with a
A Characterization of 0-epi Maps with a Degree
✍ Elena Giorgieri; Martin VΓ€th πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 174 KB

The paper was written in the framework of a DFG project (Az. AP 40-15/1). The main ideas were discussed while the second author was invited professor at the University of Rome ''Tor Vergata.'' Financial support by the DFG and the CNR is gratefully acknowledged.