Some Results of n-EP Operators on Hilbert Spaces

Menkad, Safa; Elgues, Anissa

doi:10.28924/2291-8639-22-2024-78

Research Article

Some Results of n-EP Operators on Hilbert Spaces

Safa Menkad*
Anissa Elgues

* Corresponding author

Abstract

Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H and n∈N. An operator T∈B(H) with closed range, is called n-EP operator if Tⁿ commutes with T⁺. In this paper, we present some new characterizations of n-EP operators, using Moore-penrose and Drazin inverse. Also, the problem of determining when the product of two operators is n-EP will be considered. As a consequence, we generalize a famous result on products of normal operators, due to I. Kaplansky to n-EP operators.

How to Cite

S. Menkad, A. Elgues, Some Results of n-EP Operators on Hilbert Spaces, Int. J. Anal. Appl. 22 (2024), 78. https://doi.org/10.28924/2291-8639-22-2024-78

BibTeX

@article{Menkad2024,
  author  = {Menkad, Safa and Elgues, Anissa},
  title   = {Some Results of n-EP Operators on Hilbert Spaces},
  journal = {Int. J. Anal. Appl.},
  volume  = {22},
  year    = {2024},
  pages   = {78},
  doi     = {10.28924/2291-8639-22-2024-78}
}

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