On (n,k)-quasiparanormal operators

Jiangtao Yuan; Guoxing Ji

Studia Mathematica (2012)

  • Volume: 209, Issue: 3, page 289-301
  • ISSN: 0039-3223

Abstract

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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 ) ≥ | | 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.

How to cite

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Jiangtao Yuan, and Guoxing Ji. "On (n,k)-quasiparanormal operators." Studia Mathematica 209.3 (2012): 289-301. <http://eudml.org/doc/286198>.

@article{JiangtaoYuan2012,
abstract = {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 $||T^\{1+n\}(T^\{k\}x)||^\{1/(1+n)\} ||T^\{k\}x||^\{n/(1+n)\} ≥ ||T(T^\{k\}x)||$ 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.},
author = {Jiangtao Yuan, Guoxing Ji},
journal = {Studia Mathematica},
keywords = {quasiparanormal and paranormal operators; SVEP; finite ascent; isolated spectral point; Riesz idempotent},
language = {eng},
number = {3},
pages = {289-301},
title = {On (n,k)-quasiparanormal operators},
url = {http://eudml.org/doc/286198},
volume = {209},
year = {2012},
}

TY - JOUR
AU - Jiangtao Yuan
AU - Guoxing Ji
TI - On (n,k)-quasiparanormal operators
JO - Studia Mathematica
PY - 2012
VL - 209
IS - 3
SP - 289
EP - 301
AB - 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 $||T^{1+n}(T^{k}x)||^{1/(1+n)} ||T^{k}x||^{n/(1+n)} ≥ ||T(T^{k}x)||$ 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.
LA - eng
KW - quasiparanormal and paranormal operators; SVEP; finite ascent; isolated spectral point; Riesz idempotent
UR - http://eudml.org/doc/286198
ER -

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