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On a class of generalized Fredholm operators, VII

Schmoeger C.

Demonstratio Mathematica

2000

Vol. 33, nr 1

123-130

On a class of generalized Fredholm operators, III

Schmoeger C.

Demonstratio Mathematica

1998

Vol. 31, nr 4

723-733

In [4] and [5] we have investigated the following class of bounded linear operators on an infinite-dimensional complex Banach space X: (fi)g(X) = {T zawiera się L(X) : there is some S zawiera się L(X) such that TST = T and I - ST - TS is Fredholm}. In this paper we continue these investigations. We shall prove some results concerning the ascent and the descent of an operator in (fi)g (X). Furthermore, we shall prove a spectral mapping property of the generalized Fredholm spectrum.

On a class of generalized Fredholm operators, II

Schmoeger C.

Demonstratio Mathematica

1998

Vol. 31, nr 4

705-722

For an infinite-dimensional complex Banach space X let L(X) denote the set of all bounded linear operators on X. The set g(X) of generalized Fredholm operators is defined as g(X) = {T L(X) : there is some S L(X) such that TST = T and 1 - ST - TS is Fredholm}. In [6] we have investigated this class of operators. In the present paper we continue these ivestigations.