Generalizations of Reid inequality-Reference-Cited by-同舟云学术

Generalizations of Reid inequality

Published:2018-11-20 Issue:6 Volume:68 Page:1439-1446
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Dehimi Souheyb¹,Mortad Mohammed Hichem²

Affiliation:

1. University of Mohamed El Bachir El Ibrahimi , Bordj Bou Arreridj , Algeria

2. Department of Mathematics , University of Oran , 1 Ahmed Ben Bella, B.P. 1524, El Menouar , Oran , 31000 , Algeria

Abstract

Abstract In this paper, we improve the famous Reid inequality related to linear operators. Some monotony results for positive operators are also established with a different approach from what is known in the existing literature. Lastly, Reid’s (and Halmos-Reid’s) inequalities are extended to unbounded operators.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0193/pdf

Reference10 articles.

1. Dehimi, S.—Mortad, M. H.: Right (or left) invertibility of bounded and unbounded operators and applications to the spectrum of products, Complex Anal. Oper. Theory 12(3) (2018), 589–597. 10.1007/s11785-017-0687-z.

2. Halmos, P. R.: A Hilbert Space Problem Book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967.

3. Kato, T.: Perturbation Theory for Linear Operators, 2nd edition, Springer, 1980.

4. Kittaneh, F.: Notes on some inequalities for Hilbert space operators, Publ. Res. Inst. Math. Sci. 24(2) (1988), 283–293.

5. Lin, C.-S.: Inequalities of Reid type and Furuta, Proc. Amer. Math. Soc. 129(3) (2001), 855–859.

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