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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Factorization of operators on Banach space


Author: Mary R. Embry
Journal: Proc. Amer. Math. Soc. 38 (1973), 587-590
MSC: Primary 47A05
DOI: https://doi.org/10.1090/S0002-9939-1973-0312287-8
MathSciNet review: 0312287
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Abstract: In this paper it is shown that if $ D$ and $ E$ are continuous linear operators on a Banach space $ X$, then the following are equivalent: (i) $ B$ is a right factor of $ A$, (ii) $ B$ majorizes $ A$ and (iii) the range of $ {B^\ast}$ contains the range of $ {A^\ast}$.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0312287-8
Keywords: Factorization of operators, majorization of operators, range inclusion of operators
Article copyright: © Copyright 1973 American Mathematical Society