Generalization of and#945; and#946; normal and m paranormal operators

Abstract

In this thesis, the first chapter discusses the introduction to newlinefunctional analysis, motivation behind this research and the objectives. newlineSecond chapter is an preliminary containing the definitions and results of newlineoperators acting on Hilbert space and semi-Hilbertian space. A short newlinediscussion on composition operators on 2 L space has been done. In chapter newlineIII, quasi- and#61480;and#61537;,and#61538; and#61481; -normal operators are studied We newlineobtain algebraic and spectral properties for quasi- and#61480;and#61537;,and#61538; and#61481; -normal. Further, newlineinequalities concerning the numerical radius and norm of quasi- and#61480;and#61537;,and#61538; and#61481; -normal newlineare characterized. Examples are given to show the inclusion relations newlinebetween the classes of operators. In chapter IV, new branches for normal newlineoperators defined as and#61480;and#61537;,and#61538; and#61481; -normaland#61644; quasi- and#61480;and#61537;,and#61538; and#61481; -normaland#61644;m-quasi-totally- newlineand#61480;and#61537;,and#61538; and#61481; -normal Algebraic and spectral properties are studied. In chapter newlineVII, structural properties of m-quasi- and#61480;and#61537;,and#61538; and#61481;-normal and m-quasi-totally- and#61480;and#61537;,and#61538; and#61481; newline-normal operators acting on semi-Hilbertian spaces are discussed. newlineInequalities concerning the A-numerical radius and A-operator norm of mquasi- newlineand#61480;and#61537;,and#61538; and#61481;-A-normal operators are stated. In chapter VIII, quasi- and#61480;and#61537;,and#61538; and#61481;- newlinenormal composition operator, (p,q)-quasi-M*-paranormal composition newlineoperator and (p,q)-quasi-M-paranormal composition operator on 2 L space are newlinecharacterized. Weighted quasi- and#61480;and#61537;,and#61538; and#61481;-normal composition operator, (p,q)- newlinequasi-M*-paranormal composition operator and (p,q)-quasi-M-paranormal newlinecomposition operator on 2 L space are also characterized.