On (n,k)-quasiparanormal operators

Jiangtao Yuan; Guoxing Ji

Studia Mathematica, Tome 209 (2012), p. 289-301 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $| | T^{1 + n} (T^{k} x) {| |}^{1 / (1 + n)} | | T^{k} {x | |}^{n / (1 + n)} \geq | | T (T^{k} x) | |$ 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 part and Riesz idempotents for k-quasiparanormal operators.

Publié le : 2012-01-01

Zbl 1262.47032

EUDML-ID : urn:eudml:doc:286198

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Jiangtao Yuan; Guoxing Ji. On (n,k)-quasiparanormal operators. Studia Mathematica, Tome 209 (2012) pp. 289-301. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-3-6/