PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Studia Mathematica

1998 | 129 | 2 | 185-196
Tytuł artykułu

### An ideal characterization of when a subspace of certain Banach spaces has the metric compact approximation property

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
C.-M. Cho and W. B. Johnson showed that if a subspace E of $ℓ_p$, 1 < p < ∞, has the compact approximation property, then K(E) is an M-ideal in ℒ(E). We prove that for every r,s ∈ ]0,1] with $r^2 + s^2 < 1$, the James space can be provided with an equivalent norm such that an arbitrary subspace E has the metric compact approximation property iff there is a norm one projection P on ℒ(E)* with Ker P = K(E)^{⊥} satisfying ∥⨍∥ ≥ r∥Pf∥ + s∥φ - Pf∥ ∀⨍ ∈ ℒ(E)*. A similar result is proved for subspaces of upper p-spaces (e.g. Lorentz sequence spaces d(w, p) and certain renormings of $L^p$).
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
185-196
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-08-04
poprawiono
1997-10-04
Twórcy
autor
autor
Bibliografia
• [1] E. M. Alfsen and E. G. Effros, Structure in real Banach spaces. Parts I and II, Ann. of Math. 96 (1972), 98-173.
• [2] J. C. Cabello and E. Nieto, On properties of M-ideals, Rocky Mountain J. Math., to appear.
• [3] J. C. Cabello, E. Nieto and E. Oja, On ideals of compact operators satisfying the M(r,s)-inequality, J. Math. Anal. Appl., to appear.
• [4] C.-M. Cho and W. B. Johnson, A characterization of subspaces X of $l_p$ for which K(X) is an M-ideal in L(X), Proc. Amer. Math. Soc. 93 (1985), 466-470.
• [5] D. Van Dulst, Reflexive and Superreflexive Banach spaces, Math. Centre Tracts 102, Amsterdam, 1978.
• [6] M. Feder and P. Saphar, Spaces of compact operators and their dual spaces, Israel J. Math. 21 (1975), 38-49.
• [7] G. Godefroy, N. J. Kalton, and P. D. Saphar, Unconditional ideals in Banach spaces, Studia Math. 104 (1993), 13-59.
• [8] G. Godefroy and D. Saphar, Duality in spaces of operators and smooth norms in Banach spaces, Illinois J. Math. 32 (1988), 672-695.
• [9] P. Harmand and Å. Lima, Banach spaces which are M-ideals in their biduals, Trans. Amer. Math. Soc. 283 (1984), 253-264.
• [10] P. Harmand, D. Werner and W. Werner, M-ideals in Banach Spaces and Banach Algebras, Lecture Notes in Math. 1547, Springer, Berlin, 1993.
• [11] J. Hennefeld, M-ideals, HB-subspaces, and compact operators, Indiana Univ. Math. J. 28 (1979), 927-934.
• [12] J. Johnson, Remarks on Banach spaces of compact operators, J. Funct. Anal. 32 (1979), 304-311.
• [13] N. J. Kalton, M-ideals of compact operators, Illinois J. Math. 37 (1993), 147-169.
• [14] Å. Lima, Property (wM*) and the unconditional metric compact approximation property, Studia Math. 113 (1995), 249-263.
• [15] E. Oja, On the uniqueness of the norm-preserving extension of a linear functional in the Hahn-Banach theorem, Izv. Akad. Nauk Est. SSR Ser. Fiz. Mat. 33 (1984), 424-438 (in Russian).
• [16] E. Oja, Strong uniqueness of the extension of linear continuous functionals according to the Hahn-Banach theorem, Mat. Zametki 43 (1988), 237-246 (in Russian); English transl.: Math. Notes 43 (1988), 134-139.
• [17] E. Oja and D. Werner, Remarks on M-ideals of compact operators on $X ⨁_p X$, Math. Nachr. 152 (1991), 101-111.
• [18] R. Payá and W. Werner, An approximation property related to M-ideals of compact operators, Proc. Amer. Math. Soc. 111 (1991), 993-1001.
• [19] R. R. Phelps, Uniqueness of Hahn-Banach extensions and unique best approximation, Trans. Amer. Math. Soc. 95 (1960), 238-255.
Typ dokumentu
Bibliografia
Identyfikatory