FELLAG ARIOUAT, Ayyoub2026-05-262026-05-262026http://dspace.univ-chlef.dz/handle/123456789/2451THESIS For obtaining the LMD doctorate degree Specialty: Operator TheoryThe 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.Quasi-normal operator of order nk-quasi-normal operator of order nWeyl’s TheoremThesis