Left-right fredholm and left-right browder linear relations

Abstract

In this paper we introduce the notions of left (resp. right) Fredholm and left (resp. right) Browder linear relations. We construct a Kato-type decomposition of such linear relations. The results are then applied to give another decomposition of a left (resp. right) Browder linear relation T in a Banach space as an operator-like sum T = A + B, where A is an injective left (resp. a surjective right) Fredholm linear relation and B is a bounded finite rank operator with certain properties of commutativity. The converse results remain valid with certain conditions of commutativity. As a consequence, we infer the characterization of left (resp. right) Browder spectrum under finite rank operator. 2010 Mathematics Subject Classification. Primary 47A06 Keywords. Ascent and descent of a linear relation, left and right Fredholm linear relations, left and right Browder linear relations, left and right Browder spectrum.

Characterization of some Classes Related to the Class of Browder Linear Relations

“…A study of left and right Browder linear relations has been carried by a number of authors in the recent past (see [5], [7], [9]). In a recent paper of (2016) [7], the authors prove that a left (right) Browder linear relation T in a Banach space can be expressed in the form T = A + B where A is an injective (onto) left (right) Fredholm linear relation and B is a bounded finite rank operator with BT ⊂ T B.…”