D-hyponormal and D-quasi-hyponormal Operators

Authors

  • Nadia Mesbah Larbi Tebessi University
  • Hadia Messaoudene Larbi Tebessi University

DOI:

https://doi.org/10.26713/cma.v13i3.1708

Keywords:

Drazin inverse, D-hyponormal operator, D-quasi-hyponormal operator, Fuglede-Putnam theorem

Abstract

New classes of operators named D-hyponormal, and D-quasi-hyponormal are introduced in this paper. Some basic properties of these operators are presented. An investigation of extensions of the Fuglede-Putnam theorem for D-hyponormal operators is given.

Downloads

Download data is not yet available.

Author Biographies

Nadia Mesbah, Larbi Tebessi University

Department of Mathematics and Computer Science, Laboratory of Mathematics, Informatics and Systems (LAMIS), Larbi Tebessi University

Hadia Messaoudene, Larbi Tebessi University

Faculty of Economics Sciences and Management, Laboratory of Mathematics, Informatics and Systems (LAMIS), Larbi Tebessi University

References

A. Bachir and M. W. Altanji, An asymmetric Putnam-Fuglede theorem for (p,k)-quasiposinormal operators, International Journal of Contemporary Mathematical Sciences 11(4) (2016), 165 – 172, DOI: 10.12988/IJCMS.2016.51051.

A. N. Bakir and S. Mecheri, Another version of Fuglede-Putnam theorem, Georgian Mathematical Journal 16(3) (2009), 427 – 433, DOI: 10.1515/GMJ.2009.427.

A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, Vol. 15, Springer, New York (2003), DOI: 10.1007/b97366.

S. K. Berberian, Extension of a theorem of Fuglede and Putnam, Proceedings of the American Mathematical Society 71(1) (1978), 113 – 114, DOI: 10.1090/S0002-9939-1978-0487554-2.

E. A. Bishop, A duality theorem for an arbitrary operator, Pacific Journal of Mathematics 9(2) (1959), 379 – 397, DOI: 10.2140/pjm.1959.9.379.

S. L. Campbell and C. D. Meyer, Generalized Inverse of Linear Transformations, Classics in Applied Mathematics series, xxiv + 264, SIAM (2009), DOI: 10.1137/1.9780898719048.

S. R. Caradus, Operator Theory of the Generalized Inverse, Science Press, New York (2004).

J. B. Conway, A Course in Functional Analysis, 2nd edition, Graduate Texts in Mathematics series (GTM, Vol. 96) Springer-Verlag, New York (1985), DOI: 10.1007/978-1-4757-3828-5.

M. Dana and R. Yousefi, On the classes of D-normal operators and D-quasi-normal operators on Hilbert space, Operators and Matrices 12(2) (2018), 465 – 487, DOI: 10.7153/oam-2018-12-29.

M. Dana and R. Yousefi, Generalizations of some classical theorems to D-normal operators on Hilbert spaces, Journal of Inequalities and Applications 2020 (2020), Article number: 101, DOI: 10.1186/s13660-020-02367-z.

B. Fuglede, A commutativity theorem for normal operators, Proceedings of the National Academy of Sciences 36(1) (1950), 35 – 40, DOI: 10.1073/pnas.36.1.35.

T. Furuta, On relaxation of normality in the Fuglede-Putnam theorem, Proceedings of the American Mathematical Society 77(3) (1979), 324 – 328, DOI: 10.1090/S0002-9939-1979-0545590-2.

P. R. Halmos, A Hilbert Space Problem Book, Graduate Texts in Mathematics series (GTM, Vol. 19), Springer-Verlag, New York (1982), DOI: 10.1007/978-1-4684-9330-6.

K. Laursen and M. Neumann, An Introduction to Local Spectral Theory, London Mathematical Society Monographs New Series, Vol. 20, Clarendon Press, Oxford (2000).

J. S. I. Mary and P. Vijayalakshmi, Fuglede-Putnam theorem and quasi-nilpotent part of n-power operators, Tamkang Journal of Mathematics 46(2) (2015), 151 – 165, DOI: 10.5556/j.tkjm.46.2015.1665.

S. Mecheri, Finite operators, Demonstratio Mathematica 35(2) (2002), 357 – 366, DOI: 10.1515/dema-2002-0216.

H. Messaoudene, Finite operators, Journal of Mathematics and System Science 3(4) (2013), 190 – 194.

M. H. Mortad, Yet more versions of the Fuglede-Putnam theorem, Glasgow Mathematical Journal 51(3) (2009), 473 – 480, DOI: 10.1017/S0017089509005114.

C. R. Putnam, On normal operators in Hilbert space, American Journal of Mathematics 73(2) (1951), 357 – 362, DOI: 10.2307/2372180.

J. P. Williams, Finite operators, Proceedings of the American Mathematical Society 26(1) (1970), 129 – 135, DOI: 10.1090/S0002-9939-1970-0264445-6.

Downloads

Published

29-11-2022
CITATION

How to Cite

Mesbah, N., & Messaoudene, H. (2022). D-hyponormal and D-quasi-hyponormal Operators. Communications in Mathematics and Applications, 13(3), 1097–1107. https://doi.org/10.26713/cma.v13i3.1708

Issue

Vol. 13 No. 3 (2022)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.