کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4666150 1633854 2013 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On separably injective Banach spaces
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
On separably injective Banach spaces
چکیده انگلیسی

We deal with two weak forms of injectivity which turn out to have a rich structure behind: separable injectivity and universal separable injectivity. We show several structural and stability properties of these classes of Banach spaces. We provide natural examples of (universally) separably injective spaces, including L∞L∞ ultraproducts built over countably incomplete ultrafilters, in spite of the fact that these ultraproducts are never injective. We obtain two fundamental characterizations of universally separably injective spaces. (a) A Banach space EE is universally separably injective if and only if every separable subspace is contained in a copy of ℓ∞ℓ∞ inside EE. (b) A Banach space EE is universally separably injective if and only if for every separable space SS one has Ext(ℓ∞/S,E)=0Ext(ℓ∞/S,E)=0. Section 6 focuses on special properties of 1-separably injective spaces. Lindenstrauss proved in the middle sixties that, under CH, 1-separably injective spaces are 1-universally separably injective and left open the question in ZFC. We construct a consistent example of a Banach space of type C(K)C(K) which is 1-separably injective but not universally 1-separably injective.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 234, 15 February 2013, Pages 192–216
نویسندگان
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