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On (n,k)-quasiparanormal operators

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Yuan J., Ji G.

Studia Mathematica

2012

tom 209

nr 3

289-301

Let T be a bounded linear operator on a complex Hilbert space 𝓗. For positive integers n and k, an operator T is called (n,k)-quasiparanormal if $||T^{1+n}(T^{k}x)||^{1/(1+n)} ||T^{k}x||^{n/(1+n)} ≥ ||T(T^{k}x)||$ for x ∈ 𝓗. 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 part and Riesz idempotents for k-quasiparanormal operators.

Ograniczanie wyników

1 Studia Mathematica

1 Ji G.

1 Yuan J.

1 2012

Wyniki wyszukiwania

On (n,k)-quasiparanormal operators