Displaying similar documents to “Generating real maps on a biordered set”

Ascent, descent and roots of Fredholm operators

Bertram Yood (2003)

Studia Mathematica

Similarity:

Let T be a Fredholm operator on a Banach space. Say T is rootless if there is no bounded linear operator S and no positive integer m ≥ 2 such that S m = T . Criteria and examples of rootlessness are given. This leads to a study of ascent and descent whether finite or infinite for T with examples having infinite ascent and descent.

A note on the index of B -Fredholm operators

M. Berkani, Dagmar Medková (2004)

Mathematica Bohemica

Similarity:

From Corollary 3.5 in [Berkani, M; Sarih, M.; Studia Math. 148 (2001), 251–257] we know that if S , T are commuting B -Fredholm operators acting on a Banach space X , then S T is a B -Fredholm operator. In this note we show that in general we do not have error ( S T ) = error ( S ) + error ( T ) , contrarily to what has been announced in Theorem 3.2 in [Berkani, M; Proc. Amer. Math. Soc. 130 (2002), 1717–1723]. However, if there exist U , V ∈ L ( X ) such that S , T , U , V are commuting and U S + V T = I , then error ( S T ) = error ( S ) + error ( T ) , where error stands for the index of a B -Fredholm...

Operational quantities derived from the norm and generalized Fredholm theory

Manuel Gonzalez, Antonio Martinón (1991)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We introduce and study some operational quantities associated to a space ideal 𝔸 . These quantities are used to define generalized semi-Fredholm operators associated to 𝔸 , and the corresponding perturbation classes which extend the strictly singular and strictly cosingular operators, and we study the generalized Fredholm theory obtained in this way. Finally we present some examples and show that the classes of generalized semi-Fredholm operators are non-trivial for several classical space...