Abstract

This work proves that if T belong to the class M-A(n*) operator and S* is an invertible operator belonging to the same class such that TX=XS, then T*X=XS*, where X is a Hilbert-Schmidt operator.

Keywords

  • Hilbert space
  • Fuglede-Putman
  • A(n*) operators

References

  1. Berberian, S.K. Extensions of a theorem of Fuglede and Putnam. Proc. Am. Math. Soc. 71, 113–114 (1978).
  2. Braha N., Lohaj M., Marevci F. and Lohaj Sh., Some properties of paranormal and hyponormal operators, Bull. Math. Anal. Appl., V.1, Issue 2,23–35 (2009).
  3. Conway, J.B. Subnormal operators. Research notes in mathematics, 5, Pitman advanced pub. program, (1981).
  4. Dugall B.P., Jeon I.H. and Kim I.H., On ∗-paranormal contractions and properties for ∗-class A operators, Linear Alg. Appl. 436, 954–962, (2012).
  5. Furuta T., On the Class of Paranormal Operators, Proc. Jap. Acad. 43(1967), 594-59
  6. Kaplansky, I. Products of normal operators. Duke Math. J. 20(2), 257–260 (1953).
  7. Laursen K.B., Operators with finite ascent, Pacific J. Math. 152, 323–336, (1992).
  8. Mecheri S., On quasi-∗-paranormal operators, Ann. Funct. Anal 3,86–91, (2012).
  9. Mecheri.S and Makhlouf.S, Weyl Type theorems for posinormal operators, Math. Proc. Royal Irish. Acad. 108, no.1, 68–79, (2008).
  10. Panayappan.S and Radharamani. A, A Note on p-∗-paranormal Operators and Absolute k ∗ -Paranormal Operators, Int. J. Math. Anal. 2, no. 25-28, 1257–1261, (2008)
  11. Yuan, J.T., Wang, C.H. Fuglede–Putnam type theorems for (p, k)-quasihyponormal operators via hyponormal operators. J. Inequal. Appl. 2019, Article ID 122 (2019).