Characterization of some Classes Related to the Class of Browder Linear Relations (original) (raw)

Left-right Fredholm and left-right Browder linear relations

Filomat, 2015

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.

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.

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.

On regular linear relations

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 }.

Strictly singular and strictly cosingular linear relations and their conjugates

Bulletin of the Australian Mathematical Society, 2005

In this paper various conditions are given under which the strict singularity (respectively, strict cosingularity) of a linear relation implies the strict singularity (respectively, strict cosingularity) of its conjugate. Serial-fee code: 0004-9727/05 SA2.00+0.00. 2 T. Alvarez [2] for all nonzero scalars a, ft € K and X\,x 2 € D(T). The class of such relations T is denoted by LR(X, Y). If T maps the points of its domain to singletons, then T is said to be a single valued or simple operator. The graph G{T) of T e LR(X, Y) is G(T) := {(*,!/) € * x r : a; €£>(r), j / e T i } , Let X denote the completion of the normed space X. The completion T of T £ LR(X, Y) is the linear relation in LR(X, Y) whose graph is G(T). Let M be a subspace of D(T). Then the restriction T \ M is defined by G(T \ M ) := {(m,y) :meM, ye Tm). For any subspace M of X such that M n D(T) ^ 0, we write T | M = T \ M nD(T)-The inverse of T is the linear relation X 1 " 1 defined by G t T -1 ) : = {(y,x) eYxX:(x,y)e G(T)}.

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.

SOME SPECIFIC CLASSES OF RELATIONS, A REVIEW

MAT-KOL, 2018

In this paper, the concepts of several new classes of relations on sets are presented introduced by this author in the previous five years. The following classes of relations have been introduced and partly described in several his articles: the class of quasi-regular, the class of quasi-conjugative, the class of quasi-normal and the class of normally conjugative relations.

New Results on Semiclosed Linear Relations

Facta Universitatis, Series: Mathematics and Informatics

This paper has triple main objectives. The first objective is an analysis ofsome auxiliary results on closedness and boundednes of linear relations. The seconde objective is to provide some new characterization results on semiclosed linear relations. Here it is shown that the class of semiclosed linear relations is invariant under finite and countable sums, products, and limits. We obtain some fundamental new results as well as a Kato Rellich Theorem for semiclosed linear relations and essentially interesting generalizations. The last objective concern semiclosed linear relation with closed range, where we have particularly established new characterizations of closable linear relation.

Some relations including various linear operators

Making use of the Carlson-Schaffer linear operator, some subclasses of analytic functions are studied. Some relations including various linear operators are given. anzU and 9= bnzH > n=0 n=0 by f *g we denote the Hadamard product or convolution of / and g, defined by oo U*g) (z) = ^a n b n z n .