본문 바로가기
KERD
논문KCI 등재

A NOTE ON *-PARANORMAL OPERATORS AND RELATED CLASSES OF OPERATORS

Atsushi Uchiyama|Kotaro Tanahashi
대한수학회 (The Korean Mathematical Society)|2014.03|대한수학회보 (Bulletin of the KMS)|제51권 제2호|pp. 357-371

2

조회

0

다운로드

2

인용

0

참고문헌

키워드

∗-paranormalk-paranormalnormaloidthe single valued exten- sion propertyWeyl’s theorem.
주제분류수학

초록

We shall show that the Riesz idempotent E of every ∗- paranormal operator T on a complex Hilbert space H with respect to each isolated point  of its spectrum (T) is self-adjoint and satisfies EH = ker(T − ) = ker(T − )∗. Moreover, Weyl’s theorem holds for ∗-paranormal operators and more general for operators T satisfying the norm condition ∥Tx∥n ≤ ∥Tnx∥∥x∥n−1 for all x ∈ H. Finally, for this more general class of operators we find a sufficient condition such that EH = ker(T − ) = ker(T − )∗ holds.

Abstract

We shall show that the Riesz idempotent E of every ∗- paranormal operator T on a complex Hilbert space H with respect to each isolated point  of its spectrum (T) is self-adjoint and satisfies EH = ker(T − ) = ker(T − )∗. Moreover, Weyl’s theorem holds for ∗-paranormal operators and more general for operators T satisfying the norm condition ∥Tx∥n ≤ ∥Tnx∥kx∥n−1 for all x ∈ H. Finally, for this more general class of operators we find a sufficient condition such that EH = ker(T − ) = ker(T − )∗ holds.

참고문헌 (10)

  1. S. C. Arora, "On a class of operators", Glas. Mat. Ser. III, 21(41)(2), pp.381~386 (1986)
  2. B. Arun, "On k-paranormal operators", Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 20(68)(1-2), pp.37~39 (1976)
  3. B. P. Duggal, "Quasi-similar k-paranormal operators", Oper. Matrices, 5(3), pp.417~423 (2011)
  4. T. Furuta, "On the class of paranormal operators", Proc. Japan Acad. Ser. A Math. Sci, 43, pp.594~598 (1967)
  5. Y. M. Han, "A note on ∗-paranormal operators", Integral Equations Operator Theory, 49(4), pp.435~444 (2004)
  6. V. Istr˘at, "On a class of operators", Tˆohoku Math. J. (2), 18, pp.410~413 (1966)
  7. C. S. Kubrusly, "A note on k-paranormal operators", Oper. Matrices, 4(2), pp.213~223 (2010)
  8. S. M. Patel, "Contributions to the study of spectraloid operators", Ph. D, pp.1974
  9. A. Uchiyama, "On the isolated point of the spectrum of paranormal operators", Integral Equations Operator Theory, 55(1), pp.145~151 (2006)
  10. A. Uchiyama, "Bishop’s property ( ) for paranormal operators", Oper. Matrices, 3(4), pp.517~524 (2009)

관련 논문AI추천

A NOTE ON WEYL’S THEOREM FOR -PARANORMAL OPERATORS김안현대한수학회 · 대한수학회논문집2012 · 제27권 제3호On $n$-$\ast$-paranormal operatorsMohammad H. M. Rashid대한수학회 · 대한수학회논문집2016 · 제31권 제3호On operators satisfying T*m(T*|T|2kT)1/(k+1)Tm≥*m|T|2TmMohammad H. M. Rashid대한수학회 · 대한수학회논문집2017 · 제32권 제3호Structural and spectral properties of $k$-quasi-$*$-paranormal operatorsFei Zuo, Hongliang Zuo강원경기수학회 · 한국수학논문집2015 · 제23권 제2호(m, n)-PARANORMAL OPERATORS AND (m, n) ∗-PARANORMAL OPERATORSPreeti Dharmarha, Sonu Ram대한수학회 · 대한수학회논문집2020 · 제35권 제1호Finite Operators and Weyl Type Theorems for Quasi-­*­-n-­Paranormal OperatorsFei Zuo, Wei Yan경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제4호

이 간행물의 다른 논문 (23건)

ON A SEQUENCE OF KANTOROVICH TYPE OPERATORS VIA RIEMANN TYPE q-INTEGRALAysegul Erencin, Fatma Tasdelen, Gulen Bascanbaz-Tuncapp. 303-315The second central limit theorem for martingale difference arrays전두배, Shlomo Levental, 배종식pp. 317-328Higher order nonlocal nonlinear boundary value problems for fractional differential equationsRahmat Ali Khanpp. 329-338Ding projective modules with respect to a semidualizing moduleZhongkui Liu, Limin Wang, Chunxia Zhangpp. 339-356Cohen-Macaulay modules over Noetherian local ringsKamal Bahmanpourpp. 373-386
원문 보기