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1995 | 113 | 3 | 249-263
Tytuł artykułu

Property (wM*) and the unconditional metric compact approximation property

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The main objective of this paper is to give a simple proof for a larger class of spaces of the following theorem of Kalton and Werner. (a) X has property (M*), and (b) X has the metric compact approximation property Our main tool is a new property (wM*) which we show to be closely related to the unconditional metric approximation property.
Słowa kluczowe
Czasopismo
Rocznik
Tom
113
Numer
3
Strony
249-263
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-05-30
poprawiono
1994-09-21
Twórcy
autor
  • Department of Mathematics, Agder College 65, Tordenskjoldsgate, N-4604 Kristiansand, Norway , aasvaldl@adh.no
Bibliografia
  • [1] E. Alfsen and E. Effros, Structure in real Banach spaces, Parts I and II, Ann. of Math. 96 (1972), 98-173.
  • [2] F. F. Bonsall and J. Duncan, Numerical Ranges II, London Math. Soc. Lecture Note Ser. 10, Cambridge University Press, 1973.
  • [3] P. G. Casazza and N. J. Kalton, Notes on approximation properties in separable Banach spaces, in: P. F. X. Müller and W. Schachermayer (eds.), Geometry of Banach Spaces, Proc. Conf. Strobl 1989, London Math. Soc. Lecture Note Ser. 158, Cambridge University Press, 1990, 49-63.
  • [4] H. S. Collins and W. Ruess, Weak compactness in spaces of compact operators and of vector-valued functions, Pacific J. Math. 106 (1983), 45-71.
  • [5] J. Diestel, Sequences and Series in Banach Spaces, Springer, 1984.
  • [6] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc. Providence, R.I., 1977.
  • [7] M. Feder and P. Saphar, Spaces of compact operators and their dual spaces, Israel J. Math. 21 (1975), 38-49.
  • [8] G. Godefroy, N. J. Kalton and P. D. Saphar, Unconditional ideals in Banach spaces, Studia Math. 104 (1993), 13-59.
  • [9] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
  • [10] P. Harmand and Å. Lima, Banach spaces which are M-ideals in their biduals, Trans. Amer. Math. Soc. 283 (1983), 253-264.
  • [11] P. Harmand, D. Werner and W. Werner, M-ideals in Banach Spaces and Banach Algebras, Lecture Notes in Math. 1547, Springer, Berlin, 1993.
  • [12] K. John, On a result of J. Johnson, preprint, 1993.
  • [13] J. Johnson, Remarks on Banach spaces of compact operators, J. Funct. Anal. 32 (1979), 304-311.
  • [14] N. Kalton, Spaces of compact operators, Math. Ann. 208 (1974), 267-278.
  • [15] N. Kalton, M-ideals of compact operators, Illinois J. Math. 37 (1993), 147-169.
  • [16] N. Kalton and D. Werner, Property (M), M-ideals, and almost isometric structure of Banach spaces, preprint, 1993.
  • [17] Å. Lima, Intersection properties of balls and subspaces in Banach spaces, Trans. Amer. Math. Soc. 227 (1977), 1-62.
  • [18] Å. Lima, On M-ideals and best approximation, Indiana Univ. Math. J. 31 (1982), 27-36.
  • [19] Å. Lima, The metric approximation property, norm-one projections and intersection properties of balls, Israel J. Math. 84 (1993), 451-475.
  • [20] Å. Lima, E. Oja, T. S. S. R. K. Rao and D. Werner, Geometry of operator spaces, Michigan Math. J., to appear.
  • [21] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Ergeb. Math. Grenzgeb. 92, Springer, Berlin, 1977.
  • [22] E. Oja, A note on M-ideals of compact operators, Acta et Comment. Univ. Tartuensis 960 (1993), 75/92.
  • [23] R. Phelps, Convex Functions, Monotone Operators and Differentiability, Lecture Notes in Math. 1364, Springer, 1989.
  • [24] D. Werner, Denting points in tensor products of Banach spaces, Proc. Amer. Math. Soc. 101 (1987), 122-126.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv113i3p249bwm
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