A factorization theorem for compact operators
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- by Daniel J. Randtke PDF
- Proc. Amer. Math. Soc. 34 (1972), 201-202 Request permission
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
- Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955), Chapter 1: 196 pp.; Chapter 2: 140 (French). MR 75539
- J. Lindenstrauss and L. Tzafriri, On the complemented subspaces problem, Israel J. Math. 9 (1971), 263–269. MR 276734, DOI 10.1007/BF02771592
- Dan Randtke, Characterization of precompact maps, Schwartz spaces and nuclear spaces, Trans. Amer. Math. Soc. 165 (1972), 87–101. MR 305009, DOI 10.1090/S0002-9947-1972-0305009-1
Additional Information
- © Copyright 1972 American Mathematical Society
- 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