Some Properties of Strictly Quasi-Fredholm Linear Relations (original) (raw)
Related papers
On strictly quasi-Fredholm linear relations and semi-B-Fredholm linear relation perturbations
Filomat
In this paper we introduce the set of strictly quasi-Fredholm linear relations and we give some of its properties. Furthermore, we study the connection between this set and some classes of linear relations related to the notions of ascent, essentially ascent, descent and essentially descent. The obtained results are used to study the stability of upper semi-B-Fredholm and lower semi-B-Fredholm linear relations under perturbation by finite rank operators.
On k-Strictly Quasi-Fredholm Linear Relations
Mathematica Pannonica
In this paper, we introduce and study the class of k-strictly quasi-Fredholm linear relations on Banach spaces for nonnegative integer k. Then we investigate its robustness through perturbation by finite rank operators.
Quasi-Fredholm linear relations in Hilbert spaces
Filomat, 2017
In this paper we obtain some results concerning the ascent and descent of a quasi-Fredholm relation in a Hilbert space and we analyze the behaviour of a polynomial in a quasi-Fredholm relation in a Hilbert space.
Quantities related to upper and lower semi-Fredholm type linear relations
Bulletin of the Australian Mathematical Society, 2002
Certain norm related functions of linear operators are considered in the very general setting of linear relations in normed spaces. These are shown to be closely related to the theory of strictly singular, strictly cosingular, F+ and F-linear relations. Applications to perturbation theory follow. Serial-fee code: 0004-9727/02 SA2.00+0.00.
The Class of B-Fredholm Linear Relations
Complex Analysis and Operator Theory, 2014
We establish in this paper a Kato-type decomposition of quasi-Fredholm relations on Banach spaces. This generalizes the corresponding result of Labrousse for Hilbert space relations. The result is then applied to study and give some properties of the class of B-Fredholm linear relations.
On the perturbation of semi-Fredholm relations with complemented ranges and null spaces
Acta Mathematica Sinica, English Series, 2010
Multivalued semi-Fredholm type linear operators with complemented ranges and null spaces are introduced. Conditions are obtained under which the classes given are stable under compact, strictly singular and strictly cosingular additive perturbations. We adher to the notation and terminology of the book [3]: X and Y are normed spaces, B X the closed unit ball of X, X the dual space of X and P(X) denotes the class of all closed finite-codimensional subspaces of X. If M is a subspace of X, then M ⊥ := {x ∈ X : x (x) = 0, x ∈ M }.
Fredholm theory for demicompact linear relations
Applied General Topology
We first attempt to determine conditions on a linear relation T such that μT becomes a demicompact linear relation for each μ ∈ [0,1)(see Theorems 2.4 and 2.5). Second, we display some results on Fredholm and upper semi-Fredholm linear relations involving a demicompact one(see Theorems 3.1 and 3.2). Finally, we provide some results in which a block matrix of linear relations becomes a demicompact block matrix of linear relations (see Theorems 4.2 and 4.3).
Acta Mathematica Sinica, English Series, 2012
Multivalued semi-Fredholm type linear operators with complemented ranges and null spaces are introduced. Conditions are obtained under which the classes given are stable under compact, strictly singular and strictly cosingular additive perturbations. We adher to the notation and terminology of the book [3]: X and Y are normed spaces, B X the closed unit ball of X, X the dual space of X and P(X) denotes the class of all closed finite-codimensional subspaces of X. If M is a subspace of X, then M ⊥ := {x ∈ X : x (x) = 0, x ∈ M }.
On essentially semi regular linear relations
Linear Algebra and its Applications, 2017
The characterization of bounded essentially semi regular operators in terms of Kato decomposition of finite type was studied by several authors. In this paper, we extend this characterization to the case of essentially semi regular linear relations. We also give other characterization of such linear relations. Further, we apply the obtained results to analyse the stability of the class of essentially semi regular linear relations under additional operator perturbations. Finally, as an application, we get some useful connections between the Fredholm spectrum and the essentially semi regular spectrum of linear relations.
2007
We show the existence of Banach spaces X, Y such that the set of strictly singular oper-ators (X,Y) (resp., the set of strictly cosingular operators (X,Y)) would be strictly included in F+(X,Y) (resp., F−(X,Y)) for the nonempty class of closed densely defined upper semi-Fredholm operatorsΦ+(X,Y) (resp., for the nonempty class of closed densely defined lower semi-Fredholm operators Φ−(X,Y)). Copyright © 2007 A. Dehici and K. Saoudi. This is an open access article distributed un-der the Creative Commons Attribution License, which permits unrestricted use, distri-bution, and reproduction in any medium, provided the original work is properly cited. 1.