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On (n,k)-quasi class Q Operators


Abstract


Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class of operators: (n,k)-quasi class Q operators, superclass of (n,k)-quasi paranormal operators. An operator T is said to be (n,k)-quasi class Q if it satisfies
for all x\in H and for some nonnegative integers n and k. We prove the basic structural properties of this class of operators. It will be proved that If T 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 (n,k)-quasi class Q does not have SVEP property. In the last section we also characterize the (n,k)-quasi class Q composition operators on Fock spaces.


DOI Code: 10.1285/i15900932v39n2p39

Keywords: $(n,k)$-quasi class $Q$; $(n,k)$-quasi paranormal operators; SVEP property; Fock space; composition operators

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