Factorization of operators on Banach space-Reference-Cited by-同舟云学术

Factorization of operators on Banach space

Published:1973 Issue:3 Volume:38 Page:587-590
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Embry Mary R.

Abstract

In this paper it is shown that if D D and E E are continuous linear operators on a Banach space X X , then the following are equivalent: (i) B B is a right factor of A A , (ii) B B majorizes A A and (iii) the range of B ∗ {B^\ast } contains the range of A ∗ {A^\ast } .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1973-038-03/S0002-9939-1973-0312287-8/S0002-9939-1973-0312287-8.pdf

Reference4 articles.

1. On majorization, factorization, and range inclusion of operators on Hilbert space;Douglas, R. G.;Proc. Amer. Math. Soc.,1966

2. R. G. Douglas, Addendum for “Majorization, factorization, and range inclusion" (unpublished).

3. Investigation concerning positive definite continued fractions;MacNerney, J. S.;Duke Math. J.,1959

4. Two-sided division in the ring of operators;Šmul′jan, Ju. L.;Mat. Zametki,1967

Cited by 28 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Range inclusion and diagonalization of complex symmetric operators;Canadian Journal of Mathematics;2024-04-04

2. Maps preserving the Douglas solution of operator equations;Journal of Mathematical Analysis and Applications;2022-03

3. Observability and null-controllability for parabolic equations in $ L_p $-spaces;Mathematical Control and Related Fields;2022

4. On exact controllability and complete stabilizability for linear systems;V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics;2021-11-29

5. Regularization of the factorization method applied to diffuse optical tomography;Inverse Problems;2021-11-24