NEW MAJORIZATION FOR BOUNDED LINEAR OPERATORS IN HILBERT SPACES

Document Type : Original Manuscript

Authors

Department of Pure Mathematics, University of Shahrekord, P.O. Box 115, Shahrekord, Iran.

Abstract

‎This work aims to introduce and investigate a preordering in B(H),‎
‎the Banach space of all bounded linear operators defined on a complex‎
‎Hilbert space H. It is called strong majorization and denoted by S≺sT, for‎
‎S,T∈B(H). The strong majorization follows majorization defined by Barnes‎, ‎but not vice versa‎.
‎If S≺sT, then S inherits some properties of T. ‎‎‎
‎ The strong majorization will be extended for the d-tuple of operators in B(H)d and‎
‎is called joint strong majorization denoted by S≺jsT, for S,T∈B(H)d. We show that‎
‎some properties of strong majorization are satisfied for joint strong majorization‎.

Keywords

References

 1. B. A. Barnes, Majorization, Range inclusion, and factorization for bounded linear operators, Proc. Amer. Math. Soc., 133(1) (2004), 155–162.
 
2. M. Barraa and M. Boumazgour, Inner derivations and norm equality, Proc. Amer. Math. Soc., 130(2) (2002), 471–476.
 
3. R. Bhatia and P. Šemrl, Orthogonality of matrices and some distance problems, Linear Algebra Appl., 287(1-3) (1999), 77–85.
 
4. M. Chō and M. Takaguchi, Boundary points of joint numerical ranges, Pacific J. Math., 95(1) (1981), 27–35.
 
5. R. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc., 17 (1966), 413–415.
 
6. M. S. Moslehian and A. Zamani, Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces, Linear Algebra Appl., 591 (2020), 299–321.
 
7. A. Zamani, M. S. Moslehian, M-T Chien, and H. Nakazato, Norm-parallelism and the Davis-Wieladnt radius of Hilbert space operators, Linear Multilinear Algebra, 67(11) (2019), 2147–2158 
Journal of Algebraic Systems
Volume 11, Issue 2
January 2024
Pages 1-12

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