Results 121 to 130 of about 421,577 (266)

On the Stability of the linear Transformation in Banach Spaces. [PDF]

, 1950
Tosio Aoki
openalex   +1 more source

On Banach Spaces with Bases

Journal of Functional Analysis, 1996
AbstractWe show that a Banach spaceXhas a basis provided there are bounded linear finite rank operatorsRn: X→Xsuch that limnRnx=xfor allx∈X,RmRn=Rmin(m, n)ifm≠n, andRn−Rn−1factors uniformly throughlmnp's for somep. As an application we obtain conditions on a subsetΛ⊂Zsuch thatCΛ=closedspan{zk:k∈Λ}⊂C(T) andLΛ=closedspan{zk:k∈Λ}⊂L1(T) have bases.
openaire   +2 more sources

Discrete subgroups of normed spaces are free

Bulletin of the London Mathematical Society, EarlyView.
Abstract Ancel, Dobrowolski and Grabowski (Studia Math. 109 (1994): 277–290) proved that every countable discrete subgroup of the additive group of a normed space is free Abelian, hence isomorphic to the direct sum of a certain number of copies of the additive group of the integers.
Tomasz Kania, Ziemowit Kostana
wiley   +1 more source

Free Banach lattices over pre-ordered Banach spaces [PDF]

arXiv
We define the free Banach lattice over a pre-ordered Banach space in a category of Banach lattices of a given convexity type, and show its existence. The subsumption of a pre-ordering necessitates an approach that differs fundamentally from the known one for the free Banach lattice over a Banach space under a given convexity condition, which is a ...
arxiv  

Coarse embeddings into superstable spaces [PDF]

arXiv, 2017
Krivine and Maurey proved in 1981 that every stable Banach space contains almost isometric copies of $\ell_p$, for some $p\in[1,\infty)$. In 1983, Raynaud showed that if a Banach space uniformly embeds into a superstable Banach space, then $X$ must contain an isomorphic copy of $\ell_p$, for some $p\in[1,\infty)$.
arxiv  

Reflexive Banach spaces not isomorphic to uniformly convex spaces [PDF]

, 1941
Mahlon M. Day
openalex   +1 more source

On an Erdős similarity problem in the large

Bulletin of the London Mathematical Society, EarlyView.
Abstract In a recent paper, Kolountzakis and Papageorgiou ask if for every ε∈(0,1]$\epsilon \in (0,1]$, there exists a set S⊆R$S \subseteq \mathbb {R}$ such that |S∩I|⩾1−ε$\vert S \cap I\vert \geqslant 1 - \epsilon$ for every interval I⊂R$I \subset \mathbb {R}$ with unit length, but that does not contain any affine copy of a given increasing sequence ...
Xiang Gao, Yuveshen Mooroogen, Chi Hoi Yip   +2 more
wiley   +1 more source

Mordukhovich derivatives of the normalized duality mapping in Banach spaces [PDF]

arXiv
In this paper, we investigate some properties of the Mordukhovich derivatives of the normalized duality mapping in Banach spaces. For the underlying spaces, we consider three cases: uniformly convex and uniformly smooth Banach space lp; general Banach spaces L1 and C[0,1].
arxiv  

Locally Uniformly Convex Banach Spaces [PDF]

, 1955
A. R. Lovaglia
openalex   +1 more source

The small‐scale limit of magnitude and the one‐point property

Bulletin of the London Mathematical Society, EarlyView.
Abstract The magnitude of a metric space is a real‐valued function whose parameter controls the scale of the metric. A metric space is said to have the one‐point property if its magnitude converges to 1 as the space is scaled down to a point. Not every finite metric space has the one‐point property: to date, exactly one example has been found of a ...
Emily Roff, Masahiko Yoshinaga
wiley   +1 more source