- Tytuł:
- Unconditional ideals in Banach spaces
- Autorzy:
-
Godefroy, G.
Kalton, N.
Saphar, P. - Powiązania:
- https://bibliotekanauki.pl/articles/1292973.pdf
- Data publikacji:
- 1993
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
M-ideal
hermitian operator
unconditional convergence - Opis:
- We show that a Banach space with separable dual can be renormed to satisfy hereditarily an "almost" optimal uniform smoothness condition. The optimal condition occurs when the canonical decomposition $X*** = X^{⊥} ⊕ X*$ is unconditional. Motivated by this result, we define a subspace X of a Banach space Y to be an h-ideal (resp. a u-ideal) if there is an hermitian projection P (resp. a projection P with ∥I-2P∥ = 1) on Y* with kernel $X^{⊥}$. We undertake a general study of h-ideals and u-ideals. For example we show that if a separable Banach space X is an h-ideal in X** then X has the complex form of Pełczyński's property (u) with constant one and the Baire-one functions Ba(X) in X** are complemented by an hermitian projection; the converse holds under a compatibility condition which is shown to be necessary. We relate these ideas to the more familiar notion of an M-ideal, and to Banach lattices. We further investigate when, for a separable Banach space X, the ideal of compact operators K(X) is a u-ideal or an h-ideal in ℒ(X) or K(X)**. For example, we show that K(X) is an h-ideal in K(X)** if and only if X has the "unconditional compact approximation property" and X is an M-ideal in X**.
- Źródło:
-
Studia Mathematica; 1993, 104, 1; 13-59
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł