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AIMS Mathematics

2020, Volume 5, Issue 6: 7458-7466. doi: 10.3934/math.2020477
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Research article

A Fuglede-Putnam property for N-class A(k) operators

  • 1.
    Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia
  • 2.
    Government Arts College, Coimbatore, Tamilnadu, India
  • 3.
    Department of Mathematics, College of Science, University of Bisha, Bisha, Saudi Arabia
  • Received: 06 May 2020 Accepted: 17 September 2020 Published: 22 September 2020

  • MSC : 47A30, 47B47

  • This paper studies the Fuglede-Putnam's property for $N$-class $A(k)$ operators and $\mathcal{Y}$ class operators. Some range-kernel orthogonality results of the generalized derivation induced by the above classes of operators are given.

    Citation: Ahmed Bachir, Durairaj Senthilkumar, Nawal Ali Sayyaf. A Fuglede-Putnam property for N-class A(k) operators[J]. AIMS Mathematics, 2020, 5(6): 7458-7466. doi: 10.3934/math.2020477

    Related Papers:

  • This paper studies the Fuglede-Putnam's property for $N$-class $A(k)$ operators and $\mathcal{Y}$ class operators. Some range-kernel orthogonality results of the generalized derivation induced by the above classes of operators are given.


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    [1] A. Bachir, F. Lombarkia, Fuglede-Putnam Theorem for w-hyponormal operators, Math. Inequal. Appl., 4 (2012), 777-786.
    [2] A. Bachir, S. Mecheri, Some Properties of ($\mathcal{Y}$) class operators, Kyungpook Math. J., 49 (2009), 203-209.
    [3] A. Bachir, A. Segres, Asymmetric Putnam-Fuglede Theorem for (n, k)-quasi-*-Paranormal Operators, Symmetry, 11 (2019), 1-14.
    [4] S. K. Berberian, Approximate proper vectors, Proc. Am. Math. Soc., 13 (1962), 111-114.
    [5] R. G. Douglas, On majoration, factorization, and range inclusion of operators on Hilbert space, Proc. Am. Math. Soc., 17 (1966), 413-415.
    [6] S. Mecheri, K. Tanahashi, A. Uchiyama, Fuglede-Putnam theorem for p-hyponormal or class $\mathcal{Y}$ operators, Bull. Korean Math. Soc., 43 (2006), 747-753.
    [7] C. R. Putnam, On normal operators in Hilbert space, Am. J. Math., 73 (1951), 357-362.
    [8] M. Radjabalipour, An extension of Putnam-Fuglede Theorem for Hyponormal Operators, Math. Z., 194 (1987), 117-120.
    [9] D. Senthilkumar, S. Shylaja, *-Aluthge transformation and adjoint of *-Aluthge transformation of N-class A(k) operators, Math. Sci. Int. Res. J., 53 (2015), 1-6.
    [10] D. Senthilkumar, S. Shylaja, Weyl's theorems for N-class A(k) operators and algebraically N-class A(k) operators, (communicated).
    [11] J. G. Stamfli, B. Wadhwa, An asymmetric Putnam-Fuglede theorem for dominant operators, Indian Univ. Math. J., 35 (1976), 359-365.
    [12] K. Tanahashi, On the converse of the Fuglede-Putnam Theorem, Acta Sci. Math. (Szeged), 43 (1981), 123-125.
    [13] A. Uchiyama, T. Yoshino, On the class $\mathcal{Y}$ operators, Nihonkai Math. J., 8 (1997), 179-194.
    [14] A. Uchiyama, K. Tanahashi, Fuglede-Putnam's theorem for p-hyponormal or log-hyponormal operators, Glasg. Math. J., 44 (2002), 397-410.
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  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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