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On certain quantities in Fredholm-operator theory and Mil’man’s isometry spectrum. (English) Zbl 0659.47014

We look at the following two quantities in the theory of Fredholm operators, which were introduced by M. Schechter [Indiana Univ. Mat. J. 21, 1061-1071 (1972; Zbl 0274.47007)] and B. Gramsch [Über analytische Störungen und den Index von Fredholmoperatoren auf Banach-Räumen, Univ. of Maryland (1969)]: \[ \Gamma (T):=\inf_{M\subset X}\| T|_ M\|,\quad \Delta (T):=\sup_{M\subset X}\inf_{N\subset M}\| T|_ N\|. \] Here T is a continuous linear operator from a Banach space X to a Banach space Y (i.e. \(T\in {\mathcal L}(X,Y))\) and M, N are closed infinite dimensional subspaces of X.

MSC:

47A53 (Semi-) Fredholm operators; index theories
47A10 Spectrum, resolvent

Citations:

Zbl 0274.47007