Invariant means on Abelian groups capture complementability of Banach spaces in their second duals
نویسندگان
چکیده
Let $X$ be a Banach space. Then is complemented in the bidual $X^{**}$ if and only there exists an invariant mean $\ell _\infty (G, X)\to X$ with respect to free Abelian group $G$ of rank equal cardinality $X^{**}$, this happens
منابع مشابه
Locally Uniformly Convex Norms in Banach Spaces and Their Duals
It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm that is itself locally uniformly convex.
متن کاملShift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups
We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...
متن کاملin translation: translators on their work and what it means
کتاب در باب ترجمه، اثر استر آلن و سوزان برنوفسکی منتشر شده در ماه می 2013 توسط نشریه کلمبیا است. نویسندگان در این کتاب به بررسی 18 مترجم با در نظر گرفتن نقش آثاری که این مترجمان ترجمه کرده اند میپردازند. کتاب به دو بخش تقسیم میشود: " مترجم در جهان" و " کار مترجم" این دو بخش مقالات همیشگی ترجمه و موقعیت خاص ادبیات بیگانه در جهان وسیع امروزی را مورد خطاب قرار میدهد. در این کتاب مقالات متعددی از ن...
ON BANACH SPACES WHOSE DUALS ARE ISOMORPHIC TO l1(Γ)
In this paper we present new characterizations of Banach spaces whose duals are isomorphic to l1(Γ), extending results of Stegall, Lewis-Stegall and Cilia-D’Anna-Gutiérrez.
متن کاملMore Abelian Groups with Free Duals
In answer to a question of A. Blass, J. Irwin and G. Schlitt, a subgroup G of the additive group Zω is constructed whose dual, Hom(G,Z), is free abelian of rank 2א0 . The question of whether Zω has subgroups whose duals are free of still higher rank is discussed, and some further classes of subgroups of Zω are noted.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2021
ISSN: ['0039-3223', '1730-6337']
DOI: https://doi.org/10.4064/sm200706-15-1