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A BERBERIAN TYPE EXTENSION OF FUGLEDE-PUTNAM THEOREM FOR QUASI-CLASS A OPERATORS

전인호|김인현
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2008.12|한국수학논문집 (Korean Journal of Mathematics)|제16권 제4호|pp. 583-587

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참고문헌

키워드

quasi-class A operatorHilbert-Schmidt classFuglede-Putnam theorem.
주제분류수학

초록

Let L(H ) denote the algebra of bounded linear oper- ators on a separable in¯nite dimensional complex Hilbert space H . We say that T 2 L(H ) is a quasi-class A operator if T*jT2jT ¸ T*jTj2T: In this paper we prove that if A and B are quasi-class A operators, and B¤ is invertible, then for a Hilbert-Schmidt operator X AX = XB implies A*X = XB¤*

Abstract

Let L(H ) denote the algebra of bounded linear oper- ators on a separable in¯nite dimensional complex Hilbert space H . We say that T 2 L(H ) is a quasi-class A operator if T*jT2jT ¸ T*jTj2T: In this paper we prove that if A and B are quasi-class A operators, and B¤ is invertible, then for a Hilbert-Schmidt operator X AX = XB implies A*X = XB¤*

참고문헌 (11)

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  3. S. L. Campbell, "On k-qusihyponormal operators", Math. Japon- ica, 23, pp.185~189 (1978)
  4. T. Furuta, "On relaxation of normality in the Fuglede-Putnam theorem", Proc. Amer. Math. Soc, 77, pp.324~328 (1979)
  5. T. Furuta, "Invitation to Linear Operators" (2001), Taylor and Francis
  6. T. Furuta, "A subclass of paranormal operators includ- ing class of log-hyponormal and several related classes", Scientiae Mathematicae, 1, pp.389~403 (1998)
  7. In Ho Jeon, "On operators with an absolute value condition", 대한수학회보, 41(4), pp.617~627 (2004), 대한수학회
  8. I. H. Jeon, "On operators satisfying T¤jT2jT", T¤jTj2T Lin. Alg. Appl, 418, pp.854~862 (2006)
  9. M. Y. Lee, "An extension of the Fuglede-Putnam theorem to p- quasihyponormal", Bull. Korean Math. Soc, 35, pp.319~324 (1998)
  10. J. R. Ringrose, "Compact non-self-adjoint operators" (1971), Van Nostrand Reinhold Co
  11. A. Uchiyama, "Fuglede-Putnam's theorem for log-hyponormal or p-hyponormal operators", Glasgow Math. Jour, 44, pp.397~410 (2002)

관련 논문AI추천

ON PROPERTIES OF QUASI-CLASS A OPERATORS이재원, 전인호강원경기수학회 · 한국수학논문집2008 · 제16권 제3호A Note on Subnormal and Hyponormal DerivationsVasile Lauric경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2008 · 제48권 제2호WEYL’S THEOREM, TENSOR PRODUCT, FUGLEDE-PUTNAM THEOREM AND CONTINUITY SPECTRUM FOR k-QUASI CLASS A ∗ n OPERATORSIlmi Hoxha, Naim Latif Braha대한수학회 · 대한수학회지2014 · 제51권 제5호On quasi-class A operators김인현, 전인호, B. P. Duggal강원경기수학회 · 한국수학논문집2011 · 제19권 제2호A study on generalized quasi-class A operators김건호, 전인호강원경기수학회 · 한국수학논문집2009 · 제17권 제2호On k-quasi-class A contractions김인현, 전인호강원경기수학회 · 한국수학논문집2014 · 제22권 제1호

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