Research Article

Commutable Matrix-Valued Functions and Operator-Valued Functions

Volume: 3 Number: 4 December 22, 2020
Abdelaziz Maouche *
PDF Download
Communications in Advanced Mathematical Sciences Cover Communications in Advanced Mathematical Sciences
EN

Commutable Matrix-Valued Functions and Operator-Valued Functions

Abstract

A simple expression is established for an analytic commutable matrix-valued function. Then a characterization of two by two functional commutative matrices is proven. Finally, a family of analytic normal compact operators on a Hilbert space, which commute with their derivatives, is shown to be functionally commutative.

Keywords

Riesz projection, Analytic matrix-valued function, Commutable matrices, Eigenvalue, Holomorphic operator-valued function, Resolvent, Spectrum

Supporting Institution

Sultan Qaboos university

References

  1. [1] B. Aupetit, A Primer On Spectral Theory, Universitext, Springer-Verlag, 1991.
  2. [2] H. Baumgartel, Analytic Perturbation Theory for Matrices and Operators, Operator Theory: Advances and Applications, 15, Birkhauser, 1985.
  3. [3] K. Clancy, I. Gohberg, Factorization of matrix functions and singular integral operators, Oper. Theory Adv. Appl., 3, Birkhauser Verlag (Basel) 1981.
  4. [4] J. Dieudonne, Sur un theoreme de Schwertfeger, Ann. Polon. Math. 24(1974), 87 - 88.
  5. [5] J.C. Evard, Conditions for a vector subspace E(t) and for a projector P(t) not to depend on t: , Lin. Alg. Appl. 91(1987), 121-131.
  6. [6] J. C. Evard, On matrix functions which commute with their derivative, Lin. Alg. Appl. 68(1985), 145 - 178.
  7. [7] S. Goff, Hermitian function matrices which commute with their derivative, Lin. Alg. Appl. 36(1981), 33 - 40.
  8. [8] I. Gohberg, J. Leiter, Holomorphic Operator Functions of one Variable and Applications, Oper. Theory Adv. Appl., 192, 2009.
  9. [9] I. Gohberg, S. Goldberg, M.A. Kaashoek, Classes of linear operators, 1, Birkhauser 1990.
  10. [10] T. Kato, Perturbation Theory for Linear Operators, Springer, 1980.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Publication Date

December 22, 2020

Submission Date

June 28, 2020

Acceptance Date

December 18, 2020

Published in Issue

Year 2020 Volume: 3 Number: 4

DOI

https://doi.org/10.33434/cams.759336

IZ

https://izlik.org/JA67RM87CN

Cite

RIS / Bibtex
APA
Maouche, A. (2020). Commutable Matrix-Valued Functions and Operator-Valued Functions. Communications in Advanced Mathematical Sciences, 3(4), 225-235. https://doi.org/10.33434/cams.759336
AMA
1.Maouche A. Commutable Matrix-Valued Functions and Operator-Valued Functions. Communications in Advanced Mathematical Sciences. 2020;3(4):225-235. doi:10.33434/cams.759336
Chicago
Maouche, Abdelaziz. 2020. “Commutable Matrix-Valued Functions and Operator-Valued Functions”. Communications in Advanced Mathematical Sciences 3 (4): 225-35. https://doi.org/10.33434/cams.759336.
EndNote
Maouche A (December 1, 2020) Commutable Matrix-Valued Functions and Operator-Valued Functions. Communications in Advanced Mathematical Sciences 3 4 225–235.
IEEE
[1]A. Maouche, “Commutable Matrix-Valued Functions and Operator-Valued Functions”, Communications in Advanced Mathematical Sciences, vol. 3, no. 4, pp. 225–235, Dec. 2020, doi: 10.33434/cams.759336.
ISNAD
Maouche, Abdelaziz. “Commutable Matrix-Valued Functions and Operator-Valued Functions”. Communications in Advanced Mathematical Sciences 3/4 (December 1, 2020): 225-235. https://doi.org/10.33434/cams.759336.
JAMA
1.Maouche A. Commutable Matrix-Valued Functions and Operator-Valued Functions. Communications in Advanced Mathematical Sciences. 2020;3:225–235.
MLA
Maouche, Abdelaziz. “Commutable Matrix-Valued Functions and Operator-Valued Functions”. Communications in Advanced Mathematical Sciences, vol. 3, no. 4, Dec. 2020, pp. 225-3, doi:10.33434/cams.759336.
Vancouver
1.Abdelaziz Maouche. Commutable Matrix-Valued Functions and Operator-Valued Functions. Communications in Advanced Mathematical Sciences. 2020 Dec. 1;3(4):225-3. doi:10.33434/cams.759336

Creative Commons License   The published articles in CAMS are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License..