On -quasi class Operators

Abstract

Let be a bounded linear operator on a complex Hilbert space . In this paper we introduce a new class of operators: -quasi class operators, superclass of -quasi paranormal operators. An operator is said to be -quasi class if it satisfies

for all and for some nonnegative integers and . We prove the basic structural properties of this class of operators. It will be proved that If has a no non-trivial invariant subspace, then the nonnegative operator

is a strongly stable contraction. In section 4, we give some examples which compare our class with other known classes of operators and as a consequence we prove that -quasi class does not have SVEP property. In the last section we also characterize the -quasi class composition operators on Fock spaces.