On unbounded order weakly demicompact operators (original) (raw)
Spectral Properties Involving Generalized Weakly Demicompact Operators
Mediterranean Journal of Mathematics
In this article, we introduce the notion of polynomial demicompactness and we use it to give some results on Fredholm operators and to establish a fine description of some essential spectra of a closed densely defined linear operator. Our work is a generalization of many known ones in the literature.
Characterization of Relatively Demicompact Operators by Means of Measures of Noncompactness
The Korean Mathematical Society, 2018
In this paper, we show that an unbounded S 0-demicompact linear operator T with respect to a bounded linear operator S 0 , acting on a Banach space, can be characterized by the Kuratowskii measure of noncompactness. Moreover, some other quantities related to this measure provide sufficient conditions to the operator T to be S 0-demicompact. The obtained results are used to discuss the connection with Fredholm and upper Semi-Fredholm operators.
Some results on order weakly compact operators
Mathematica Bohemica, 2009
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
L-weakly and M-weakly demicompact operators on Banach lattices
Filomat
In this paper, we introduce and investigate new concepts of L-weakly and M-weakly demicompact operators. Let E be a Banach lattice. An operator T : E ? E is called L-weakly demicompact, if for every norm bounded sequence (xn) in BE such that {xn ? Txn, n ? N} is an L-weakly compact subset of E, we have {xn, n ? N} is an L-weakly compact subset of E. Additionally, an operator T : E ? E is called M-weakly demicompact if for every norm bounded disjoint sequence (xn) in E such that ?xn ?Txn? ? 0, we have ?xn? ? 0. L-weakly (resp. M-weakly) demicompact operators generalize known classes of operators which are L-weakly (resp. M-weakly) compact operators. We also elaborate some properties of these classes of operators.
Spectral properties for generalized weakly S-demicompact operators
Linear and Multilinear Algebra, 2020
In this paper, we introduce the concept of generalized weakly S-demicompact operators with respect to a weakly closed linear operator S. We study the general setting of Fredholm theory. We give some perturbation results on the behaviour of relative essential spectra of the sum of two bounded linear operators by means of the relative essential spectra of each one. A characterization of generalized weakly S-demicompact operators by means of measures of weak noncompactness is given. Moreover, we impose some sufficient conditions on the inputs of a closable block operator matrix to ensure the generalized weak S-demicompactness of its closure.
Indagationes Mathematicae, 1990
In the following let E and F be arbitrary Banach lattices and assume that Fis Dedekind complete.
On the Weakly Precompact and Unconditionally Converging Operators
Glasgow Mathematical Journal, 2006
In this paper we present some results about wV (weak property V of Pełczyński) or property wV * (weak property V * of Pełczyński) in Banach spaces. We show that E has property wV if for any reflexive subspace F of E * , ⊥ F has property wV. It is shown that G has property wV if under some condition K w * (E * , F *) contains the dual of G. Moreover, it is proved that E * contains a copy of c 0 if and only if E contains a copy of 1 where E has property wV *. Finally, the identity between L(C(, E), F) and WP(C(, E), F) is investigated.
The Relationship between M-Weakly Compact Operator and Order Weaky Compact Operator
2013
In this note, we will show that the class of order weakly compact operators bigger than the class of M-weakly compact operators. Under a new condition, we will show that each M-weakly compact operator is an order weakly compact operator. We will show that, if Banach lattice E be an AM-space with unit and has the property (b), then the class of M-weakly compact operators from E into Banach space Y coincides with that of order weakly compact operators from E into Y. Also we establish some relationship between M-weakly compact operators and weakly compact operators and b-weakly compact operators and order weakly compact operators.