Extensions of the results on powers of -hyponormal and -hyponormal operators.
Powers of class operators.
Spectrum of class operators.
Aluthge transforms of -hyponormal operators.
On (n,k)-quasiparanormal operators
Let T be a bounded linear operator on a complex Hilbert space . For positive integers n and k, an operator T is called (n,k)-quasiparanormal if for x ∈ . The class of (n,k)-quasiparanormal operators contains the classes of n-paranormal and k-quasiparanormal operators. We consider some properties of (n,k)-quasiparanormal operators: (1) inclusion relations and examples; (2) a matrix representation and SVEP (single valued extension property); (3) ascent and Bishop’s property (β); (4) quasinilpotent...
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