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Finite-dimensional decompositions of Banach spaces with (p,q)-estimates

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Rozprawy Matematyczne tom/nr w serii: 263 wydano: 1987
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Warianty tytułu
Abstrakty
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CONTENTS
Introduction................................................................................................................................5
I. Basic notations and definitions................................................................................................7
II. Basic properties of finite-dimensional decompositions with (p,q)-estimates............................8
III. A construction of f.d.d.'s satisfying (p,q)-estimates and its geometric applications...............13
IV. An application of the construction of f.d.d.'s with (p,q)-estimates to universal spaces.........24
V. Examples..............................................................................................................................34
Open problems.........................................................................................................................39
References...............................................................................................................................40
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 263
Liczba stron
41
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCLXIII
Daty
wydano
1987
Twórcy
  • Instytut Matematyki UMCS, pl. M. Curie-Skłodowskiej 2, 20-031 Lublin, Polska
Bibliografia
  • [1] S. Banach, Théorie des operations linéaires, Monografie Matematyczne 1, Warszawa 1932.
  • [2] J. Bourgain, On separable Banach spaces, universal for all separable reflexive spaces, Proc. Amer. Math. Soc. 79 (1980), 241-246.
  • [3] J. Bourgain, On the Banach-Saks property in Lebesgue spaces, preprint Vrije Universiteit Brussel 1979-10.
  • [4] P. Casazza, On a geometric condition related to boundedly complete bases and normal structure in Banach spaces, Proc. Amer. Math. Soc. 36 (1972), 443-447.
  • [5] M. M. Day, Reflexive spaces not isomorphic to uniformly convex spaces, Bull. Amer. Math. Soc. 47 (1941), 313-317.
  • [6] J. Diestel, Geometry of Banach spaces - Selected topics, Lecture Notes in Math. 485, Springer, Berlin and New York 1975.
  • [7] J. Diestel, J. J. Uhl, Vector measures, Math. Surveys 15, Amer. Math. Soc. 1977.
  • [8] E. Dubinski, A. Pełczyński, H. P. Rosenthal, On Banach spaces X for which $Π₂(ℒ_{∞},X) = B(ℒ_{∞},X)$, Studia Math. 44 (1972), 617-634.
  • [9] V. J. Gurarii, N. J. Gurarii, On bases in uniformly convex and uniformly smooth Banach spaces, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 210-215.
  • [10] R. C. James, Super-reflexive spaces with bases, Pacific J. Math. 41 (1972), 409-419.
  • [11] W. B. Johnson, Factoring compact operators, Israel J. Math. 9 (1971), 337-345.
  • [12] W. B. Johnson, H. P. Rosenthal, M. Zippin, On bases, finite dimensional decompositions and weaker structures in Banach spaces, Israel J. Math. 9 (1971), 488-506.
  • [13] W. B. Johnson, A. Szankowski, Complementably universal Banach spaces, Studia Math. 58 (1976), 91-97.
  • [14] W. B. Johnson, M. Zippin, On subspaces of quotients of $(∑G_n)_{l_p}$ and $(∑G_n)_{c_0}$ Israel J. Math. 13 (1972), 311-316.
  • [15] M. I. Kadec, On complementably universal Banach spaces, Studia Math. 40 (1971), 85-89.
  • [16] L. J. Krivine, Sous-espaces de dimension fini des espaces de Banach réticulés, Ann. of Math. 104 (1976), 1-29.
  • [17] J. Lindenstrauss, Notes on Klee's paper "Polyhedral sections of convex bodies", Israel J. Math. 4 (1966), 235-242.
  • [18] J. Lindenstrauss, L. Tzafiri, Classical Banach spaces: I. Sequence spaces, Springer, Ergebnisse, Berlin-Heidelberg-New York 1977.
  • [19] J. Lindenstrauss, L. Tzafiri, Classical Banach spaces: II. Function spaces, Springer, Ergebnisse, Berlin-Heidelberg-New York 1979.
  • [20] A. R. Lovaglia, Locally uniformly convex Banach spaces. Trans. Amer. Math. Soc. 78 (1955), 225-238.
  • [21] A. Pełczyński, Universal bases, Studia Math. 32 (1969), 247-268.
  • [22] A. Pełczyński, Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basis, Studia Math. 40 (1971), 239-242.
  • [23] A. Pełczyński, P. Wojtaszczyk, Banach spaces with finite dimensional expansions of identity and universal bases of finite dimensional subspaces, Studia Math. 40 (1971), 91-108.
  • [24] G. Pisier, Martingales with values in uniformly convex spaces, Israel J. Math. 20 (1975), 326-350.
  • [25] S. Prus, Finite dimensional decompositions with p-estimates and universal Banach spaces, Bull. Acad. Pol. Sei. 31 (1983), 281 288.
  • [26] H. P. Rosenthal, On a theorem of J. L. Krivine concerning local finite representability of $l^p$ in general Banach spaces, J. Funct. Anal. 28 (1978), 197-225.
  • [27] G. Schechtman, On Pełczyński's paper "Universal bases", Israel J. Math. 22 (1975), 181-184.
  • [28] I. Singer, Bases in Banach spaces, I, Springer, Berlin-Heidelberg-New York 1970.
  • [29] W. Szlenk, The non-existence of a separable reflexive Banach space universal for all separable reflexive Banach spaces, Studia Math. 30 (1968), 53-61.
  • [30] P. Wojtaszczyk, On separable Banach spaces containing all separable reflexive Banach spaces, Studia Math. 37 (1970), 197-202.
  • [31] M. Zippin, Existence of universal members in certain families of bases of Banach spaces, Proc. Amer. Math. Soc. 26 (1970), 294-301.
Języki publikacji
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Identyfikator YADDA
bwmeta1.element.zamlynska-abf10900-8379-4476-bda5-b698fe3de799
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ISBN
83-01-07892-8
ISSN
0012-3862
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