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Factorization of operators on Banach space

Author: Mary R. Embry
Journal: Proc. Amer. Math. Soc. 38 (1973), 587-590
MSC: Primary 47A05
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}$.

References [Enhancements On Off] (What's this?)

  • [1] R. G. Douglas, On majorization, factorization and range inclusion of operators on Hilbert space, Proc Amer. Math. Soc. 17 (1966), 413-415. MR 34 #3315. MR 0203464 (34:3315)
  • [2] R. G. Douglas, Addendum for ``Majorization, factorization, and range inclusion" (unpublished).
  • [3] J. S. Mac Nerney, Investigation concerning positive definite continued fractions, Duke Math. J. 26 (1959), 663-677. MR 22 #8107. MR 0117326 (22:8107)
  • [4] Ju. L. Šmul'jan, Two-sided division in the ring of operators, Mat. Zametki 1 (1967), 605-610 = Math. Notes 1 (1967), 400-403. MR 36 #729. MR 0217640 (36:729)

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Keywords: Factorization of operators, majorization of operators, range inclusion of operators
Article copyright: © Copyright 1973 American Mathematical Society

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