arXiv subjects

Farida Lombarkia

Publications and source records attributed to Farida Lombarkia.

3 recordsLinked to original sources

arXiv2025

Solvability of The Operator Equations $ AX-XB=C $ and $ AX-YB=C $

This paper provides new necessary and sufficient conditions for the solvability to the operator equations $ AX-XB=C$ and $AX-YB=C,$ where $A $ and $B $ are group invertible operators defined on an infinite dimensional Hilbert space. In addition, the general solutions to the equation $AX-YB=C,$ are derived in terms of group inverse of $ A $ and $ B $. As a consequence, new necessary and sufficient conditions for the solvability to the operator equation $ AYB-Y=C,$ are derived.

math.FA↗

arXiv2016

Asymmetric Fuglede Putnam's Theorem for operators reduced by their eigenspaces

Fuglede-Putnam Theorem have been proved for a considerably large number of class of operators. In this paper by using the spectral theory, we obtain a theoretical and general framework from which Fuglede-Putnam theorem may be promptly established for many classes of operators.

math.FA↗

arXiv2014

Some spectral properties for generalized derivations

Given Banach spaces $\mathcal{X}$ and $\mathcal{Y}$ and Banach space operators $A\in L(\mathcal{X})$ and $B\in L(\mathcal{Y}).$ The generalized derivation $δ_{A,B} \in L(L(\mathcal{Y},\mathcal{X}))$ is defined by $δ_{A,B}(X)=(L_{A}-R_{B})(X)=AX-XB$. This paper is concerned with the problem of the transferring the left polaroid property, from operators $A$ and $B^{*}$ to the generalized derivation $δ_{A,B}$. As a consequence, we give necessary and sufficient conditions for $δ_{A,B}$ to satisfy generalized a-Browder's theorem and generalized a-Weyl's theorem. As application, we extend some recent results concerning Weyl type theorems.

math.SP↗