Remarks on the classical Banach operator ideals
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- by J. Diestel and B. Faires PDF
- Proc. Amer. Math. Soc. 58 (1976), 189-196 Request permission
Abstract:
Sufficient conditions are given that the $\lambda$-tensor product of two operators be weakly compact.References
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- A. Grothendieck, Sur les applications linéaires faiblement compactes d’espaces du type $C(K)$, Canad. J. Math. 5 (1953), 129–173 (French). MR 58866, DOI 10.4153/cjm-1953-017-4
- Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955), Chapter 1: 196 pp.; Chapter 2: 140 (French). MR 75539 —, Resumé de le théorie mé trique des produits tensoriels topologiques, Bol. Soc. Mat. São Paulo 8 (1956), 1-79.
- J. R. Holub, Tensor product bases and tensor diagonals, Trans. Amer. Math. Soc. 151 (1970), 563–579. MR 279564, DOI 10.1090/S0002-9947-1970-0279564-2
- J. R. Holub, Compactness in topological tensor products and operator spaces, Proc. Amer. Math. Soc. 36 (1972), 398–406 (1973). MR 326458, DOI 10.1090/S0002-9939-1972-0326458-7
- A. Pełczyński, Projections in certain Banach spaces, Studia Math. 19 (1960), 209–228. MR 126145, DOI 10.4064/sm-19-2-209-228
- A. Pełczyński, Banach spaces on which every unconditionally converging operator is weakly compact, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 641–648. MR 149295
- A. Pełczyński, On strictly singular and strictly cosingular operators. I. Strictly singular and strictly cosingular operators in $C(S)$-spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 31–36. MR 177300
- A. Pełczyński, On strictly singular and strictly cosingular operators. II. Strictly singular and strictly cosingular operators in $L(\nu )$-spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 37–41. MR 177301
- A. Pełczyński and Z. Semadeni, Spaces of continuous functions. III. Spaces $C(\Omega )$ for $\Omega$ without perfect subsets, Studia Math. 18 (1959), 211–222. MR 107806, DOI 10.4064/sm-18-2-211-222
- Albrecht Pietsch, Theorie der Operatorenideale (Zusammenfassung), Wissenschaftliche Beiträge der Friedrich-Schiller-Universität Jena, Friedrich-Schiller-Universität, Jena, 1972 (German). MR 0361822
- Haskell P. Rosenthal, On complemented and quasi-complemented subspaces of quotients of $C(S)$ for Stonian $S$, Proc. Nat. Acad. Sci. U.S.A. 60 (1968), 1165–1169. MR 231185, DOI 10.1073/pnas.60.4.1165 C. Stegall, Banach spaces whose duals contain ${l_1}(\Gamma )$ with applications to the study of dual ${L_1}(\mu )$ spaces (preprint).
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 58 (1976), 189-196
- MSC: Primary 47B05; Secondary 46M05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0454701-6
- MathSciNet review: 0454701