Factorization of operators on Banach space
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- by Mary R. Embry PDF
- Proc. Amer. Math. Soc. 38 (1973), 587-590 Request permission
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 ${A^\ast }$.References
- R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413–415. MR 203464, DOI 10.1090/S0002-9939-1966-0203464-1 R. G. Douglas, Addendum for “Majorization, factorization, and range inclusion" (unpublished).
- J. S. MacNerney, Investigation concerning positive definite continued fractions, Duke Math. J. 26 (1959), 663–677. MR 117326
- Ju. L. Šmul′jan, Two-sided division in the ring of operators, Mat. Zametki 1 (1967), 605–610 (Russian). MR 217640
Additional Information
- © Copyright 1973 American Mathematical Society
- 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