dc.contributor.author | Muthengi, Frewdrick. | |
dc.contributor.author | Musundi, Sammy. | |
dc.contributor.author | Aywa, Shem. | |
dc.date.accessioned | 2019-05-08T13:39:40Z | |
dc.date.available | 2019-05-08T13:39:40Z | |
dc.date.issued | 2015-03-18 | |
dc.identifier.issn | 0039-3223 | |
dc.identifier.uri | http://erepository.kibu.ac.ke/handle/123456789/901 | |
dc.description.abstract | 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**. | en_US |
dc.language.iso | en | en_US |
dc.publisher | Instytut matematyczny polskiej akademi nauk | en_US |
dc.rights | Attribution-NonCommercial-ShareAlike 3.0 United States | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/us/ | * |
dc.subject | M-ideal | en_US |
dc.subject | Hermitian operator | en_US |
dc.subject | Unconditional convergence | en_US |
dc.title | On unconditional banach space ideal property | en_US |
dc.type | Article | en_US |