The Kato decomposition of quasi-Fredholm relations

By J. Labrousse, Adrian Sandovici, H. D. de Snoo, H. Winkler. 2010

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Quasi-Fredholm relations of degree d is an element of N in Hilbert spaces are defined in terms of conditions on their ranges and kernels. They are completely characterized in terms of an algebraic decomposition with a quasi-Fredholm relation of degree 0 and a nilpotent operator of degree d. The adjoint of a quasi-Fredholm relation of degree d is an element of N is shown to be quasi-Fredholm relation of degree d is an element of N. The class of quasi-Fredholm relations contains the semi-Fredholm relations. Earlier results for quasi-Fredholm operators and semi-Fredholm operators are included.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3a95a234790e3901a106ac529ca4d091a68794f6

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H. D. Snoo
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Citations in the corpus

Componentwise and Cartesian decompositions of linear relations (2009, background): “ B. Hence this implication follows by symmetry. The following observation, based on Lemma 2.10, goes back to Yu.L. Shmul’jan [35]. A weaker version for so-called range space relations can be found in [25]. Theorem 2.11. Let Abe a closed relation in a Hilbert space H. Then (i) domAclosed ⇐⇒ domA∗ clo”