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A factorization theorem for compact operators


Author: Daniel J. Randtke
Journal: Proc. Amer. Math. Soc. 34 (1972), 201-202
MSC: Primary 47B05
DOI: https://doi.org/10.1090/S0002-9939-1972-0295135-3
MathSciNet review: 0295135
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Abstract: It is shown that every compact operator $ T:E \to F$ between Banach spaces admits a compact factorization ($ T = QP$ where $ P:E \to c$ and $ Q:c \to F$ are compact) through a closed subspace c of the Banach space $ {c_0}$ of zero-convergent sequences.


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

  • [1] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. No. 16 (1955). MR 17, 763. MR 0075539 (17:763c)
  • [2] J. Lindenstrauss and L. Tzafriri, On the complemented subspaces problem, Israel. J. Math. 9 (1971), 263-269. MR 0276734 (43:2474)
  • [3] D. J. Randtke, Characterizations of precompact maps, Schwartz spaces and nuclear spaces, Trans. Amer. Math. Soc. 165 (1972), 87-101. MR 0305009 (46:4139)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0295135-3
Keywords: Banach space, compact operator, approximation property, Hilbert space
Article copyright: © Copyright 1972 American Mathematical Society

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