P A ON (n, k)-QUASIPARANORMAL WEIGHTED COMPOSITION OPERATORS

International Journal of Mathematical Archive, 2012

An operator is said to be - quasi - paranormal operator if for every , is a natural number. In this paper, - quasi - paranormal composition operators on space and Hardy space is characterized.

This class includes the classes of paranormal operators and quasi-class A operators. In this paper, quasi-paranormal composition operators on 2 L space and Hardy space are characterized.

Bull. Korean Math. Soc, 2010

In this note, we discuss measure theoretic characterizations for weighted composition operators in some operator classes on L 2 (F) such as, p-quasihyponormal, p-paranormal, p-hyponormal and weakly hyponormal. Some examples are then presented to illustrate that weighted composition operators lie between these classes.

In this paper some classes of weighted composition operators on 2 L -spaces are characterized and their various properties are studied.

2014

An operator T is called n-normal operator if T nT ∗ = T ∗T n and n-quasinormal operator if T nT ∗T = T ∗TT n. In this paper, the conditions under which composition operators and weighted composition operators become n-normal operators and n-quasinormal operators have been obtained in terms of Radon-Nikodym derivative hn.

Annals of Functional Analysis, 2015

An operator T on a Hilbert space H is called p-quasiposinormal operator if c 2 T * (T * T) p T ≥ T * (T T *) p T where 0 < p ≤ 1 and for some c > 0. In this paper, we have obtained conditions for composition and weighted composition operators to be p-quasiposinormal operators.

Archiv der Mathematik, 2008

In this paper we study the point spectrum of the operator

2020

ABSTRACT. A necessary and sufficient condition for a bounded operator to be a composition operator is investigated in this paper. Normal, quasi-hyponormal, paranormal composition operators are characterlsed. KEY WORDS AND PHRASES. Invertible, normal, quasi-normal, hyponormal, quasi-hyponorm, paanormal composition operators. AMS (MOS) SUBJECT CLASSIFICATION (1970) CODES. Primay 47B99, Secondary 47B99. 12 In the case C is bounded and the range of C is in 2 we call it a composition operator. The symbol B(l2) denotes the Banach algebra of all bounded

Journal of Functional Analysis, 2006

Starting with a general formula, precise but difficult to use, for the adjoint of a composition operator on a functional Hilbert space, we compute an explicit formula on the classical Hardy Hilbert space for the adjoint of a composition operator with rational symbol. To provide a foundation for this formula, we study an extension to the definitions of composition, weighted composition, and Toeplitz operators to include symbols that are multiple valued functions. These definitions can be made on any Banach space of analytic functions on a plane domain, but in this work, our attention is focused on the basic properties needed for the application to operators on the standard Hardy and Bergman Hilbert spaces on the unit disk.