PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1994 | 30 | 1 | 161-174
Tytuł artykułu

On incomparability of Banach spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Several concepts of incomparability of Banach spaces have been considered in the literature, which allow one to describe some of the properties of the product of two Banach spaces as a juxtaposition of the corresponding properties of the factors. In this paper we study the relations between these concepts of incomparability, survey the main results and applications, and state some open problems.
Słowa kluczowe
Rocznik
Tom
30
Numer
1
Strony
161-174
Opis fizyczny
Daty
wydano
1994
Twórcy
  • Departamento de Matemáticas, Universidad de Cantabria, 39071 Santander, Spain
  • Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain
Bibliografia
  • [1] P. Aiena and M. González, Essentially incomparable Banach spaces and Fredholm theory, Proc. Roy. Irish Acad. 93A (1993), 49-59.
  • [2] T. Alvarez, M. González and V. M. Onieva, A note on three-space Banach space ideals, Arch. Math. (Basel) 46 (1986), 169-170.
  • [3] T. Alvarez, M. González and V. M. Onieva, Totally incomparable Banach spaces and three-space ideals, Math. Nachr. 131 (1987), 83-88.
  • [4] T. Alvarez, M. González and V. M. Onieva, Characterizing two classes of operator ideals, in: Contribuciones Matemáticas. Homenaje Prof. Antonio Plans, Univ. Zaragoza, Zaragoza, 1990, 7-21.
  • [5] J. Bourgain, New Classes of $ℒ^p$-Spaces, Lecture Notes in Math. 889, Springer, Berlin, 1981.
  • [6] J. Bourgain and F. Delbaen, A class of special $ℒ^∞$-spaces, Acta Math. 145 (1980), 155-176.
  • [7] P. G. Casazza, N. J. Kalton and L. Tzafriri, Decompositions of Banach lattices into direct sums, Trans. Amer. Math. Soc. 304 (1987), 771-800.
  • [8] J. C. Díaz, An example of Fréchet space, not Montel, without infinite dimensional normable subspaces, Proc. Amer. Math. Soc. 96 (1986), 721.
  • [9] J. Diestel and R. H. Lohman, Applications of mapping theorems to Schwartz spaces and projections, Michigan Math. J. 20 (1973), 39-44.
  • [10] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., 1977.
  • [11] A. Douady, Un espace de Banach dont le groupe linéaire n'est pas connexe, Indag. Math. 27 (1965), 787-789.
  • [12] L. Drewnowski, On minimally subspace-comparable F-spaces, J. Funct. Anal. 26 (1977), 39-44.
  • [13] I. S. Edelstein and P. Wojtaszczyk, On projections and unconditional bases in direct sums of Banach spaces, Studia Math. 56 (1976), 263-276.
  • [14] G. Emmanuele, Banach spaces in which Dunford-Pettis sets are relatively compact, Arch. Math. (Basel) 58 (1992), 477-485.
  • [15] M. González, On essentially incomparable Banach spaces, Math. Z., to appear.
  • [16] M. González and A. Martinón, Operational quantities derived from the norm and generalized Fredholm theory, Comment. Math. Univ. Carolin. 32 (1991), 645-657.
  • [17] M. González and A. Martinón, Fredholm theory and space ideals, Boll. Un. Mat. Ital. 7-B (1993), 473-488.
  • [18] M. González and V. M. Onieva, On incomparability of Banach spaces, Math. Z. 112 (1986), 581-585.
  • [19] M. González and V. M. Onieva, El problema de los tres espacios, in: Homenaje al Prof. Dr. Nácere Hayek Calil, Univ. La Laguna, La Laguna, 1990, 155-162.
  • [20] W. T. Gowers and B. Maurey, The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), 851-874.
  • [21] V. I. Gurariĭ, On openings and inclinations of subspaces of Banach spaces, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 1 (1965), 194-204 (in Russian).
  • [22] S. Heinrich, On the relation between linear n-widths and approximation numbers, J. Approx. Theory 58 (1989), 315-333.
  • [23] N. J. Kalton, Quotients of F-spaces, Glasgow Math. J. 19 (1978), 103-108.
  • [24] N. J. Kalton, B. Turett and J. J. Uhl, Jr., Basically scattered vector measures, Indiana Univ. Math. J. 28 (1979), 803-816.
  • [25] T. Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math. 6 (1958), 261-322.
  • [26] N. H. Kuiper, The homotopy type of the unitary group of Hilbert space, Topology 3 (1965), 19-30.
  • [27] A. Lavergne, Remark on sums of complemented subspaces, Colloq. Math. 41 (1979), 103-104.
  • [28] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Sequence Spaces, Springer, Berlin, 1977.
  • [29] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II. Function Spaces, Springer, Berlin, 1977.
  • [30] R. H. Lohman, An example concerning normed subspaces of locally convex spaces, Proc. Amer. Math. Soc. 41 (1973), 245-246.
  • [31] A. Martinón, Cantidades operacionales en teoría de Fredholm, Tesis Doctoral, Univ. La Laguna, 1989.
  • [32] A. Martinón, Operational quantities and classes of operators, in: Aportaciones matemáticas en memoria del Prof. V. M. Onieva, Univ. Cantabria, Santander, 1991, 227-236.
  • [33] B. S. Mityagin, The homotopy structure of the linear group of a Banach space, Russian Math. Surveys 25 (1970), 59-103.
  • [34] G. Neubauer, Der Homotopietyp der Automorphismengruppe in den Räumen $l_p$ und c₀, Math. Ann. 174 (1967), 33-40.
  • [35] 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.
  • [36] A. Pełczyński, On strictly singular and strictly cosingular operators. II. Strictly singular and strictly cosingular operators in L(ν)-spaces, ibid., 37-41.
  • [37] A. Pietsch, Operator Ideals, North-Holland, Amsterdam, 1980.
  • [38] A. Pietsch, Inessential operators in Banach spaces, Integral Equations Operator Theory 1 (1978), 589-591.
  • [39] J. Prada, On idempotent operators on Fréchet spaces, Arch. Math. (Basel) 43 (1984), 179-182.
  • [40] H. P. Rosenthal, On totally incomparable Banach spaces, J. Funct. Anal. 4 (1969), 167-175.
  • [41] H. P. Rosenthal, On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from $L^p(μ)$ to $L^r(ν)$, ibid., 176-214.
  • [42] W. Rudin, Spaces of type $H^∞ + C$, Ann. Inst. Fourier (Grenoble) 25 (1) (1975), 99-125.
  • [43] R. J. Whitley, Strictly singular operators and their conjugates, Trans. Amer. Math. Soc. 113 (1964), 252-261.
  • [44] P. Wojtaszczyk, On projections and unconditional bases in direct sums of Banach spaces II, Studia Math. 62 (1978), 193-201.
  • [45] V. P. Zahariuta, On the isomorphism of cartesian products of locally convex spaces, ibid. 46 (1973), 201-221.
  • [46] J. Zemánek, Geometric characteristics of semi-Fredholm operators and their asymptotic behaviour, ibid. 80 (1984), 219-234.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv30z1p161bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.