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.
@article{bwmeta1.element.bwnjournal-article-smv113i3p249bwm, author = {\u Asvald Lima}, title = {Property (wM*) and the unconditional metric compact approximation property}, journal = {Studia Mathematica}, volume = {113}, year = {1995}, pages = {249-263}, zbl = {0826.46013}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv113i3p249bwm} }
Lima, Ăsvald. Property (wM*) and the unconditional metric compact approximation property. Studia Mathematica, Tome 113 (1995) pp. 249-263. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv113i3p249bwm/
[00000] [1] E. Alfsen and E. Effros, Structure in real Banach spaces, Parts I and II, Ann. of Math. 96 (1972), 98-173. | Zbl 0248.46019
[00001] [2] F. F. Bonsall and J. Duncan, Numerical Ranges II, London Math. Soc. Lecture Note Ser. 10, Cambridge University Press, 1973. | Zbl 0262.47001
[00002] [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. | Zbl 0743.41027
[00003] [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. | Zbl 0488.46057
[00004] [5] J. Diestel, Sequences and Series in Banach Spaces, Springer, 1984.
[00005] [6] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc. Providence, R.I., 1977.
[00006] [7] M. Feder and P. Saphar, Spaces of compact operators and their dual spaces, Israel J. Math. 21 (1975), 38-49. | Zbl 0325.47028
[00007] [8] G. Godefroy, N. J. Kalton and P. D. Saphar, Unconditional ideals in Banach spaces, Studia Math. 104 (1993), 13-59. | Zbl 0814.46012
[00008] [9] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
[00009] [10] P. Harmand and Å. Lima, Banach spaces which are M-ideals in their biduals, Trans. Amer. Math. Soc. 283 (1983), 253-264. | Zbl 0545.46009
[00010] [11] P. Harmand, D. Werner and W. Werner, M-ideals in Banach Spaces and Banach Algebras, Lecture Notes in Math. 1547, Springer, Berlin, 1993. | Zbl 0789.46011
[00011] [12] K. John, On a result of J. Johnson, preprint, 1993.
[00012] [13] J. Johnson, Remarks on Banach spaces of compact operators, J. Funct. Anal. 32 (1979), 304-311. | Zbl 0412.47024
[00013] [14] N. Kalton, Spaces of compact operators, Math. Ann. 208 (1974), 267-278. | Zbl 0266.47038
[00014] [15] N. Kalton, M-ideals of compact operators, Illinois J. Math. 37 (1993), 147-169. | Zbl 0824.46029
[00015] [16] N. Kalton and D. Werner, Property (M), M-ideals, and almost isometric structure of Banach spaces, preprint, 1993.
[00016] [17] Å. Lima, Intersection properties of balls and subspaces in Banach spaces, Trans. Amer. Math. Soc. 227 (1977), 1-62. | Zbl 0347.46017
[00017] [18] Å. Lima, On M-ideals and best approximation, Indiana Univ. Math. J. 31 (1982), 27-36. | Zbl 0455.41016
[00018] [19] Å. Lima, The metric approximation property, norm-one projections and intersection properties of balls, Israel J. Math. 84 (1993), 451-475. | Zbl 0814.46016
[00019] [20] Å. Lima, E. Oja, T. S. S. R. K. Rao and D. Werner, Geometry of operator spaces, Michigan Math. J., to appear. | Zbl 0823.46023
[00020] [21] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Ergeb. Math. Grenzgeb. 92, Springer, Berlin, 1977. | Zbl 0362.46013
[00021] [22] E. Oja, A note on M-ideals of compact operators, Acta et Comment. Univ. Tartuensis 960 (1993), 75/92. | Zbl 1214.46005
[00022] [23] R. Phelps, Convex Functions, Monotone Operators and Differentiability, Lecture Notes in Math. 1364, Springer, 1989. | Zbl 0658.46035
[00023] [24] D. Werner, Denting points in tensor products of Banach spaces, Proc. Amer. Math. Soc. 101 (1987), 122-126. | Zbl 0647.46018