Inverses généralisés d’opérateurs non bornés

Abstract

Abstract.This paper is devoted to the definition and the study of the generalized inverses of unbounded densely defined closed operators in Banach and Hubert spaces. In this latter case an identity is established that links the orthogonal projection on the graph of an operator to the orthogonal projection on the graph of its Moore-Penrose inverse.

Compact and Finite Rank Perturbations of Closed Linear Operators and Relations in Hilbert Spaces

“…is the canonical embedding of K 1 into K. Now Propositions 2.1 and 2.3 yield the following corollary, which is a slight generalization of the main result in [12], see also [9].…”

Moore-Penrose Inverse in Kreĭn Spaces

“…These results follow directly from the properties of a * -generalized inverse and lemma 1.3 [15]. The existence of a unique maximal * -generalized inverse is now given by the following theorem:…”

“…Weakly regular operators may be connected with the notion of strict generalized inverse of Labrousse [15]. Actually, one can prove that an operator A admits a strict generalized * -inverse if and only if it is weakly regular, and in this case, the inverse is weakly regular, hence unique and precisely A + .…”

Functional characterizations of trace spaces in Lipschitz domains

“…Also, the operators (I + A * A) −1 and A(I + A * A) −1 are everywhere defined and bounded, and (I + A * A) −1 is selfadjoint. Moreover, [16,18]). In the following, we state some useful identities due to Labrousse [18] and Labrousse and Mbekhta [19].…”

“…For extensive results and applications concerning the Moore-Penrose inverse concept, we refer the reader to [8,16,18,19] and references therein. The following results are, to the best of our knowledge, new.…”