12 papers
Natural Geometry Based on the Rectilinear Plane
Mohammed Berkani
The aim of this note is to introduce natural geometry, in which the rectilinear plane is a primitive. This plane is admitted together with its rectitude, and its rectitude states t…
On Left and Right Semi-B-Fredholm Operators
Alaa Hamdan, Mohammed Berkani
To complete the study of Fredholm type operators of [10] and [11], we define in this paper the classes of left and right semi-B-Fredholm operators (Definition 3.1). Then, we prove…
Fredholm-type Operators and Index
Alaa Hamdan, Mohammed Berkani
While in \cite{HB} we studied classes of Fredholm-type operators defined by the homomorphism from onto the Calkin algebra , being a Banach space, we…
On Classes of Fredholm Type Operators
Alaa Hamdan, Mohammed Berkani
Given an idempotent in a Banach algebra and following the study in \cite{P50} of p-invertibility, we consider here left p-invertibility, right p-invertibility and p-invertibili…
Index of continuous semi-Fredholm families, regularities and semiregularities
Mohammed Berkani
In this paper, we define and index for continuous families of semi-Fredholm bounded liner operators. Moreover, we study various regularities and semiregularities of continuous fami…
Index of continuous families of bounded linear operators in Banach spaces and application
Mohammed Berkani
In this paper, we define an analytical index for continuous families of Fredholm operators parameterized by a topological space into a Banach space We also consid…