Fundamental and spectral properties of some classes of non-normal operators on a Hilbert space
Loading...
Date
2026
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Aissa NASLI BAKIR / Tayeb HADJ KADDOUR
Abstract
The purpose of this thesis is to investigate several properties of certain classes of nonnormal linear bounded operators acting on a separable complex Hilbert space specifically,
those operators that fail to commute with their adjoints. We present a collection of essential structural and spectral characteristics that extend well-known properties of normal
operators. These include
1. orthogonal decompositions,
2. restrictions concerning invariant subspaces,
3. Bishop’s property ,
4. the single-valued extension property,
5. isoloid and polaroid operators
In addition, new results are obtained regarding invariant subspaces and the behavior of
the Riesz idempotent associated with these operator classes. The methods rely mainly on
the theory of orthogonal decompositions, as well as on the study of invariant and reducing
subspaces, which together form the theoretical framework of this research.
Description
THESIS
For obtaining the LMD doctorate degree
Specialty: Operator Theory
Keywords
Quasi-normal operator of order n, k-quasi-normal operator of order n, Weyl’s Theorem