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On projective tensor products with complemented subspaces isomorphic to ℓ1(*)

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Abstract

We give new sufficient conditions in order that a projective tensor product

of Banach spaces contains complemented copies of ℓ1, which provides us new examples of this situation.

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References

  1. Castillo J.,On Banach spaces X such that L(L p ,X)=K(L p ,X). Preprint.

  2. Castillo J., López Molina J.A.,Operators defined on projective and natural tensor products. Michigan Math. J.,40 (1993), 411–415.

    Article  MATH  MathSciNet  Google Scholar 

  3. Dulst Van D.,Reflexive and superreflexive Banach spaces. Mathematical Center Tracts 102. Mathematisch Centrum. Amsterdam. 1978.

    MATH  Google Scholar 

  4. Kadec M. I., Pelczynski A.,Bases, lacunary sequences and complemented subspaces in the spaces L p . Studia Math.,21 (1962), 161–176.

    MATH  MathSciNet  Google Scholar 

  5. Kwapien S., Pelczynski A.,The main triangle projection in matrix spaces and its applications. Studia Math.,34 (1970), 43–68.

    MATH  MathSciNet  Google Scholar 

  6. Lacey H. E.,The isometric theory of classical Banach spaces. Springer Verlag. Berlin. Heidelberg. New York. 1974.

    MATH  Google Scholar 

  7. Lindenstrauss J., Tzafriri L.,Classical Banach spaces. Lecture Notes in Math. 338. Springer Verlag. Berlin. Heidelberg. New York. 1973.

    MATH  Google Scholar 

  8. Linderstrauss J., Tzafriri L.,Classical Banach spaces I. Springer Verlag. Berlin. Heidelberg. New York 1977.

    Google Scholar 

  9. López Molina J. A., Rivera M. J.,Bounded, Montel and compact operators on vector valued Köthe spaces. Results in Math.,29 (1996), 115–124.

    MATH  Google Scholar 

  10. Oja E.,Sur la réflexivité des produits tensoriels et les sous-spaces des produits tensoriels projectifs. Math. Scand.,51 (1982), 275–288.

    MATH  MathSciNet  Google Scholar 

  11. Rosenthal H. P.,On quasi-complemented subspaces of Banach spaces, with an apprendix on compactness of operators from L p(μ)to L r(ν). J. Func. Anal.,4 (1969), 176–214.

    Article  MATH  Google Scholar 

  12. Ryan R. A.,The Dunford-Pettis property and projective tensor products. Bull. Acad. Polon. Sci.,27 (1989) 373–379.

    Google Scholar 

  13. Tzafriri L.,Remarks on contractive projections in L p spaces. Israel J. Math.,7 (1969) 9–15.

    Article  MATH  MathSciNet  Google Scholar 

  14. Zaanen A. C.,Integration. North Holland. Amsterdam. 1967.

    MATH  Google Scholar 

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Authors and Affiliations

  1. E. T. S. Ingenieros Agrónomos, Camino de Vera, 46071, Valencia, Spain

    J. A. López Molina & M. J. Rivera

Authors
  1. J. A. López Molina
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  2. M. J. Rivera
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Supported in part by DGICYT, project PB91-0538.

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López Molina, J.A., Rivera, M.J. On projective tensor products with complemented subspaces isomorphic to ℓ1(*). Rend. Circ. Mat. Palermo 45, 414–420 (1996). https://doi.org/10.1007/BF02844512

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  • DOI: https://doi.org/10.1007/BF02844512

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