ISSN (Online): 2321-3418
server-injected
Mathematics and Statistics
Open Access

Some theorems on the class M-A(n*) operators on Hilbert space

DOI: 10.18535/ijsrm/v12i04.m01Β· Pages: 479-483Β· Vol. 12, No. 04, (2024)Β· Published: April 6, 2024
PDF
Views: 358 PDF downloads: 181

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 spaceFuglede-PutmanA(n*) operators1- Introduction: Let 𝐻 denote a separable complex Hilbert space characterized by the inner product <βˆ™βˆ™>

References

  1. Berberian, S.K. Extensions of a theorem of Fuglede and Putnam. Proc. Am. Math. Soc. 71, 113–114 (1978).Google Scholar β†—
  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).Google Scholar β†—
  3. Conway, J.B. Subnormal operators. Research notes in mathematics, 5, Pitman advanced pub. program, (1981).Google Scholar β†—
  4. Dugall B.P., Jeon I.H. and Kim I.H., On βˆ—-paranormal contractions and properties for βˆ—-class A operators, Linear Alg. Appl. 436, 954–962, (2012).Google Scholar β†—
  5. Furuta T., On the Class of Paranormal Operators, Proc. Jap. Acad. 43(1967), 594-59Google Scholar β†—
  6. Kaplansky, I. Products of normal operators. Duke Math. J. 20(2), 257–260 (1953).Google Scholar β†—
  7. Laursen K.B., Operators with finite ascent, Pacific J. Math. 152, 323–336, (1992).Google Scholar β†—
  8. Mecheri S., On quasi-βˆ—-paranormal operators, Ann. Funct. Anal 3,86–91, (2012).Google Scholar β†—
  9. Mecheri.S and Makhlouf.S, Weyl Type theorems for posinormal operators, Math. Proc. Royal Irish. Acad. 108, no.1, 68–79, (2008).Google Scholar β†—
  10. Panayappan.S and Radharamani. A, A Note on p-βˆ—-paranormal Operators and Absolute k βˆ— -Paranormal Operators, Int. J. Math. Anal. 2, no. 25-28, 1257–1261, (2008)Google Scholar β†—
  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).Google Scholar β†—
Author details
Shaymaa Al-shakarchi
Department of Mathematics, Faculty of Basic Education University of Kufa, Najaf, Iraq
βœ‰ Corresponding Author
πŸ‘€ View Profile β†’