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What is needed for a O-absolutely summing operator to be nuclear?

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Complex Analysis and Spectral Theory

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References

  1. A. Grothendieck. Résumé de la théorie métrique des produits tensoriels topologiques. Bol.Soc.Mat.São Paulo, 1956, 8, 1–79.

    MATH  Google Scholar 

  2. J. Lindenstrauss, A. Pełczyński. Absolutely summing operators in L p-spaces and their applications. Studia Math., 1968, 29, 275–326.

    MathSciNet  MATH  Google Scholar 

  3. A.Pietsch. Operator ideals. Berlin, 1978.

    Google Scholar 

  4. С.В.Кисляков. О пространствах с "малым" аннулятором. Зап. научн. семин. ЛОМИ, 1976, 65, 192–195.

    Google Scholar 

  5. G. Pisier. Une nouvelle classe d’espaces de Banach vérifiant le théorème de Grothendieck. Ann.Inst.Fourier, 1978, 28, N 1, 69–90.

    Article  MathSciNet  MATH  Google Scholar 

  6. Н.К.Никольский, В.П.Хавин, С.В.Хрушëв (составители и редакторы). 99 нерещённых эадач линейного и комплексного аналиэа. Зап. научн. семин. ЛОМИ, 1978, 81.

    Google Scholar 

  7. Y. Gordon, D.R. Lewis, J.R. Retherford. Banach ideals of operators with applications. J.Funct.Anal., 1973, 14, 85–129.

    Article  MathSciNet  MATH  Google Scholar 

  8. B.Maurey. Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces LP. Astérisque, 1974, 11.

    Google Scholar 

  9. S. Kwapień, A. Pełczyński. Remarks on absolutely summing translation invariant operators from the disc algebra and its dual. Michigan J.Math., 1978, 25, 173–181.

    Article  MATH  Google Scholar 

  10. S.Kwapień, A.Pełczyński. Absolutely summing operators and translation invariant spaces of functions on compact abelian groups. Inst.Mat.PAN, preprint N 162, Warszawa, 1978.

    Google Scholar 

  11. A.Pełczyński. Banach spaces of analytic functions and absolutely summing operators. AMS Regional Conference Series in Mathematics, 30, Providence, 1977.

    Google Scholar 

  12. A. Pełczyński. P-integral operators commuting with group representations and examples of quasi P-integral operators which are not P-integral. Studia Math., 1969, 33, 63–70.

    MathSciNet  MATH  Google Scholar 

  13. P.L. Duren. Theory of HP spaces. Academic Press, New York and London, 1970.

    MATH  Google Scholar 

  14. С.В.Кисляков. О рефлексивных подпространствах пространства q*A. Функц. аналиэ и его прилок., 1979, 13, № 1, 21–30.

    Google Scholar 

  15. A.Zygmund. Trigonimetric series. Vol. 1,2. Cambridge, 1959.

    Google Scholar 

  16. B.S. Mitjagin, A. Pełczyński. On the nonexistence of linear isomorphisms between Banach spaces of analytic functions of one and several complex variables. Studia Math., 1975, 56, 85–96.

    Google Scholar 

  17. B. Muckenhoupt. Weighted norm inequalities for Hardy maximal function. Trans.Amer.Math.Soc., 1972, 165, 207–226.

    Article  MathSciNet  MATH  Google Scholar 

  18. R.A. Hunt, B. Muckenhoupt, R.L. Wheeden. Weighted norm inequalities for the conjugate function and Hilbert transform. Trans.Amer.Math.Soc., 1973, 176, 227–251.

    Article  MathSciNet  MATH  Google Scholar 

  19. R.R. Coifman, C. Fefferman. Weighted norm inequalities for maximal functions and singular integrals. Studia Math., 1974, 51, N 3, 241–250.

    MathSciNet  MATH  Google Scholar 

  20. S. Szarek. On Kashin’s almost euclidean orthogonal decomposition of ℓn 1. Bull.Acad.Polon.Sci., sér.sci.math., astr. et phys., 1978, 26 N 8, 691–694.

    MathSciNet  MATH  Google Scholar 

  21. S. Szarek, N. Tomczak-Jaegermann. On nearly euclidean decompositions for some classes of Banach spaces. Compos.Math., 1980, 40, N 3, 367–385.

    MathSciNet  MATH  Google Scholar 

  22. L.Danzer, B.Grunbaum, V.Klee. Helly’s theorem and its relatives. "Convexity", Proc.sympos.pure math., vol.7, Amer.Math.Soc., Providence, 1963.

    Google Scholar 

  23. T. Figiel, S. Kwapień, A. Pełczyński. Sharp estimates for the constants of local unconditional structure of Minkowski spaces. Bull.Acad.Polon.Sci., sér. sci math., astr. et phys., 1977, 25, N 11, 1221–1226.

    MathSciNet  MATH  Google Scholar 

  24. M.I. Kadec, A. Pełczyński. Bases, lacunary sequences and complemented subspaces in the spaces LP. Studia Math., 1861/62, 21, 161–176.

    Google Scholar 

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Victor P. Havin Nikolai K. Nikol’skii

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© 1981 Springer-Verlag

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Kisliakov, S.V. (1981). What is needed for a O-absolutely summing operator to be nuclear?. In: Havin, V.P., Nikol’skii, N.K. (eds) Complex Analysis and Spectral Theory. Lecture Notes in Mathematics, vol 864. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097001

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  • DOI: https://doi.org/10.1007/BFb0097001

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