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On the tensor product of weakly compact operators

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References

  1. Carl, B., Defant, A., Ramanujan, S.: On tensor stable operator ideals. Mich. Math. J.36, 63–75 (1989)

    Article  Google Scholar 

  2. Davis, W.J., Figiel, T., Johnson, W.B., Peŀczyński, A.: Factoring weakly compact operators. J. Funct. Anal.17, 311–327 (1974)

    Article  Google Scholar 

  3. Diestel, J.: A survey of results related to the Dunford-Pettis property. In: Proceedings of the Conference on Integration, Topology, and Geometry in Linear Spaces. (Contemp. Math., vol. 2, pp. 15–60) Providence, R. I: Am. Math. Soc. 1980

    Google Scholar 

  4. Diestel, J., Faires, B.: Remarks on the classical Banach operator ideals. Proc. Am. Math. Soc.58, 189–196 (1976)

    Google Scholar 

  5. Duchoň, M.: On a tensor product of weakly compact mappings. Math. Slovaca36, 393–400 (1986)

    Google Scholar 

  6. Dunford, N., Schwartz, J.T.: Linear Operators. Part I. New York: Interscience 1967

    Google Scholar 

  7. Feder, M., Saphar, P.: Spaces of compact operators and their dual spaces. Isr. J. Math.21, 38–49 (1975)

    Google Scholar 

  8. Figiel, T.: Factorization of compact operators and applications to the approximation problem. Stud. Math.45, 191–210 (1973)

    Google Scholar 

  9. Grothendieck, A.: Sur les applications linéaires faiblement compactes d'espaces du type C(K). Can. J. Math.5, 129–173 (1953)

    Google Scholar 

  10. Grothendieck, A.: Produits tensoriels topologiques et espaces nucléaires. Mém. Am. Math. Soc.16 (1955)

  11. Holub, J.R.: Tensor product mappings. Math. Ann.188, 1–12 (1970)

    Article  Google Scholar 

  12. Holub, J.R.: Integral operators in Banach spaces. Proc. Am. Math. Soc.29, 75–80 (1971)

    Google Scholar 

  13. Holub, J.R.: Tensor product mappings. II. Proc. Am. Math. Soc.42, 437–441 (1974)

    Google Scholar 

  14. Jarchow, H.: Locally covex spaces. Stuttgart: Teubner 1981

    Google Scholar 

  15. John, K.: Personal communication.

  16. John, K.: On the compact non-nuclear operator problem. Math. Ann.287, 509–514 (1990)

    Article  Google Scholar 

  17. Lewis, D.R.: Conditional weak compactness in certain inductive tensor products. Math. Ann.201, 201–209 (1973)

    Article  Google Scholar 

  18. Pisier, G.: Factorization of linear operators and geometry of Banach spaces. (CBMS Reg. Conf. Ser., no. 60) Providence, RI: Am. Math. Soc. 1986

    Google Scholar 

  19. Pisier, G.: Counterexamples to a conjecture of Grothendieck. Acta Math.151, 181–208 (1983)

    Google Scholar 

  20. Saksman, E., Tylli, H.-O.: Weak compactness of multiplication operators on spaces of bounded linear operators. Math. Scand. (to appear)

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Racher, G. On the tensor product of weakly compact operators. Math. Ann. 294, 267–275 (1992). https://doi.org/10.1007/BF01934325

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