相关论文: On $c_0$-saturated Banach spaces

The Banach-Mazur problem, which asks if every infinite-dimensional Banach space has an infinite-dimensional separable quotient space, has remained unsolved for 85 years, but has been answered in the affirmative for special cases such as…

$C_p(X)$ denotes the space of continuous real-valued functions on a Tychonoff space $X$ endowed with the topology of pointwise convergence. A Banach space $E$ equipped with the weak topology is denoted by $E_{w}$. It is unknown whether…

Several new characterizations of the Gelfand-Phillips property are given. We define a strong version of the Gelfand-Phillips property and prove that a Banach space has this stronger property iff it embeds into $c_0$. For an infinite compact…

We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property has the unconditional tree property. Then we prove that a separable reflexive Banach space with the unconditional tree…

A recent result of Freeman, Odell, Sari, and Zheng states that whenever a separable Banach space not containing $\ell_1$ has the property that all asymptotic models generated by weakly null sequences are equivalent to the unit vector basis…

A necessary and sufficient condition for an operator space to support a multiplication making it completely isometric and isomorphic to a unital operator algebra is proved. The condition involves only the holomorphic structure of the Banach…

We prove that a WLD subspace of the space $\ell_\infty^c(\Gamma)$ consisting of all bounded, countably supported functions on a set $\Gamma$ embeds isomorphically into $\ell_\infty$ if and only if it does not contain isometric copies of…

Let $G$ be an infinite locally compact abelian group. If $X$ is Banach space, we show that if every bounded Fourier multiplier $T$ on $L^2(G)$ has the property that $T\ot Id_X$ is bounded on $L^2(G,X)$ then the Banach space $X$ is…

The main result of this paper is that the space of conformally compact Einstein metrics on a given manifold is a smooth, infinite dimensional Banach manifold, provided it is non-empty, generalizing earlier work of Graham-Lee and Biquard. We…

It is an open problem whether an infinite-dimensional amenable Banach algebra exists whose underlying Banach space is reflexive. We give sufficient conditions for a reflexive, amenable Banach algebra to be finite-dimensional (and thus a…

We show in this paper that every bijective linear isometry between the continuous section spaces of two non-square Banach bundles gives rise to a Banach bundle isomorphism. This is to support our expectation that the geometric structure of…

Necessary and sufficient conditions for a separable Banach space to be a dual space are proved. Some applications are discussed

The complemented subspace problem asks, in general, which closed subspaces $M$ of a Banach space $X$ are complemented; i.e. there exists a closed subspace $N$ of $X$ such that $X=M\oplus N$? This problem is in the heart of the theory of…

We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space $c_0$.

Let N and M be von Neumann algebras. It is proved that L^p(N) does not Banach embed in L^p(M) for N infinite, M finite, 1 < or = p < 2. The following considerably stronger result is obtained (which implies this, since the Schatten p-class…

Hereditarily indecomposable Banach spaces may have density at most continuum (Plichko-Yost, Argyros-Tolias). In this paper we show that this cannot be proved for indecomposable Banach spaces. We provide the first example of an…

We show that a (complex) $C_\sigma$-space is separably injective if and only if it is linearly isometric to the Banach space $C_0(\Omega)$ of complex continuous functions vanishing at infinity on a substonean locally compact Hausdorff space…

It is known that if $M$ is a finite-dimensional Banach space, or a strictly convex space, or the space $\ell_1$, then every non-expansive bijection $F: B_M \to B_M$ is an isometry. We extend these results to non-expansive bijections $F: B_E…

We study Hahn-Banach extensions of multilinear forms defined on Banach sequence spaces. We characterize $c_0$ in terms of extension of bilinear forms, and describe the Banach sequence spaces in which every bilinear form admits extensions to…

For a Banach space $X$ its subset $Y\subseteq X$ is called overcomplete if $|Y|=dens(X)$ and $Z$ is linearly dense in $X$ for every $Z\subseteq Y$ with $|Z|=|Y|$. In the context of nonseparable Banach spaces this notion was introduced…