Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

(m, n)-PARANORMAL OPERATORS AND (m, n)⁎-PARANORMAL OPERATORS

  • Dharmarha, Preeti (Department of Mathematics Hansraj College University of Delhi) ;
  • Ram, Sonu (Department of Mathematics University of Delhi)
  • Received : 2018.11.03
  • Accepted : 2019.03.11
  • Published : 2020.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

We introduce the notion of (m, n)-paranormal operators and (m, n)⁎-paranormal operators on Hilbert space and study their properties. We also characterize these operators. Examples of operators are given which are (m, n)-paranormal but not (m, n)⁎-paranormal, and vice-versa.

Keywords

References

  1. T. Ando, Operators with a norm condition, Acta Sci. Math. (Szeged) 33 (1972), 169-178.
  2. S. C. Arora and R. Kumar, M-paranormal operators, Publ. Inst. Math. (Beograd) (N.S.) 29(43) (1981), 5-13.
  3. S. C. Arora and J. K. Thukral, $M^{\ast}$-paranormal operators, Glas. Mat. Ser. III 22(42) (1987), no. 1, 123-129.
  4. S. C. Arora and J. K. Thukral, Quasi $^{\ast}-paranormal$ operators, Invarient subspace and Allied spaces, Narosa Publication (1990), 79-86.
  5. N. L. Braha, M. Lohaj, F. H. Marevci, and Sh. Lohaj, Some properties of paranormal and hyponormal operators, Bull. Math. Anal. Appl. 1 (2009), no. 2, 23-35.
  6. T. Furuta, On the class of paranormal operators, Proc. Japan Acad. 43 (1967), 594-598. http://projecteuclid.org/euclid.pja/1195521514 https://doi.org/10.3792/pja/1195521514
  7. V. Istratescu, On some hyponormal operators, Pacific J. Math. 22 (1967), 413-417. http://projecteuclid.org/euclid.pjm/1102992095 https://doi.org/10.2140/pjm.1967.22.413
  8. V. Istratescu, Some results on M-hyponormal operators, Math. Sem. Notes Kobe Univ. 6 (1978), no. 1, 77-86.
  9. C. S. Kubrusly and B. P. Duggal, A note on k-paranormal operators, Oper. Matrices 4 (2010), no. 2, 213-223. https://doi.org/10.7153/oam-04-10
  10. S. M. Patel, Contributions to the study of spectraloid operators, Ph. D. Thesis, Delhi Univ., 1974.