arXiv subjects

Margot Salas-Brown

Publications and source records attributed to Margot Salas-Brown.

3 recordsLinked to original sources

arXiv2023

Two classes of operators related to the perturbation classes problem

Let $SS$ and $SC$ be the strictly singular and the strictly cosingular operators acting between Banach spaces, and let $PΦ_+$ and $PΦ_+$ be the perturbation classes for the upper and the lower semi-Fredholm operators. We study two classes of operators $ΦS$ and $ΦC$ that satisfy $SS\subset ΦS \subset PΦ_+$ and $SC\subset ΦC\subset PΦ_-$. We give some conditions under which these inclusions become equalities, from which we derive some positive solutions to the perturbation classes problem for semi-Fredholm operators.

math.FA↗

arXiv2020

The perturbation classes problem for subprojective and superprojective Banach spaces

We show that the perturbation class for the upper semi-Fredholm operators between two Banach spaces X and Y coincides with the strictly singular operators when X is subprojective and that the perturbation class for the lower semi-Fredholm operators coincides with the strictly cosingular operators when Y is superprojective. Similar results were previously obtained under stronger conditions for X and Y.

math.FA↗

arXiv2016

Properties of Multiplication Operators on Köthe spaces

We make an exhaustive study of the properties of multiplication operator $M_u$ acting on Köthe spaces. We characterize the multiplication operators, acting on Köthe spaces, which are: bounded, injective, onto, bijective, Fredholm, compact, with closed range and with range finite. We also study the spectrum, the $n$-power and calculate the essential norm of $M_u$ and we study the algebra of multiplication operators.

math.FA↗