相关论文: Isomorphic classification of projective tensor pro…

We compute the Szlenk index of an arbitrary projective tensor product $C(K)\widehat{\otimes}_\pi C(L)$ of spaces $C(K), C(L)$ of continuous functions on scattered, compact, Hausdorff spaces. In particular, we show that it is simply equal to…

Galego and Samuel showed that if $K,L$ are metrizable, compact, Hausdorff spaces, then $C(K)\widehat{\otimes}_\pi C(L)$ is $c_0$-saturated if and only if it is subprojective if and only if $K$ and $L$ are both scattered. We remove the…

We study the classification of spaces of continuous functions $C(K)$ under positive linear maps. For infinite countable compacta, we show that whenever $C(K)$ and $C(L)$ are isomorphic, there exists an isomorphism $T:C(K)\to C(L)$…

In this paper we prove that the $3$-fold injective tensor product $\ell_1 \widehat{\otimes}_\varepsilon \ell_1 \widehat{\otimes}_\varepsilon \ell_1 $ is not isomorphic to any subspace of $\ell_1 \widehat{\otimes}_\varepsilon \ell_1$. This…

Let $m,n$ be positive integers with $m<n$. Under certain assumptions on the Banach space $X$, we prove that the $n$-fold projective tensor product of $X$, $\widehat{\otimes}^n_\pi X$, is not isomorphic to any subspace of any quotient of the…

In this article we prove that every isometric copy of C(L) in C(K) is complemented if L is compact Hausdorff of finite height and K is a compact Hausdorff space satisfying the extension property, i.e., every closed subset of K admits an…

In the present paper we prove that the $3$-fold projective tensor product of $c_0$, $c_{0} \widehat{\otimes}_\pi c_{0}\widehat{\otimes}_\pi c_{0}$, is not isomorphic to a subspace of $c_{0} \widehat{\otimes}_\pi c_{0}$. In particular, this…

A classical result of Cembranos and Freniche states that the C(K, X) spaces contains a complemented copy of c_0 whenever K is an infinite compact Hausdorff space and X is an infinite dimensional Banach space. This paper takes this result as…

We prove that if $K$ and $L$ are compact spaces and $C(K)$ and $C(L)$ are isomorphic as Banach spaces then $K$ has a $\pi$-base consisting of open sets $U$ such that $\bar{U}$ is a continuous image of some compact subspace of $L$. This…

Let $C_0(K, X)$ denote the space of all continuous $X$-valued functions defined on the locally compact Hausdorff space $K$ which vanish at infinity, provided with the supremum norm. If $X$ is the scalar field, we denote $C_0(K, X)$ by…

We investigate the following general problem, closely related to the problem of isomorphic classification of Banach spaces $C(K)$ of continuous real-valued functions on a compact space $K$, equipped with the supremum norm: Let $\mathcal{K}$…

We complete the classification, up to isomorphism, of the spaces of compact operators on C([1, gamma], l_p) spaces, 1<p< infinity. In order to do this, we classify, up to isomorphism, the spaces of compact operators {\mathcal K}(E, F),…

Let $X$ be an infinite compact metric space with finite covering dimension and let $\alpha, \beta : X\to X$ be two minimal homeomorphisms. We prove that the crossed product $C^*$-algebras $C(X)\rtimes_\alpha\Z$ and $C(X)\rtimes_\belta\Z$…

The classical theorems of Banach and Stone, Gelfand and Kolmogorov, and Kaplansky show that a compact Hausdorff space $X$ is uniquely determined by the linear isometric structure, the algebraic structure, and the lattice structure,…

We study the general form of isomorphisms on the algebra of compactly supported complex-valued continuous functions defined on a locally compact Hausdorff space (the proof of which works for the algebra of $C^k-$differentiable functions on…

For a compact space $K$ we denote by $C_w(K)$ ($C_p(K)$) the space of continuous real-valued functions on $K$ endowed with the weak (pointwise) topology. In this paper we address the following basic question which seems to be open: Suppose…

Assume hat a functionally Hausdorff space $X$ is a continuous image of a \v{C}ech complete space $P$ with Lindel\"of number $l(P)<\mathfrak c$. Then the following conditions are equivalent: (i) every compact subset of $X$ is scattered, (ii)…

Let $f$ and $g$ be scalar-valued, continuous functions on some topological space. We say that $g$ dominates $f$ in the compatibility ordering if $g$ coincides with $f$ on the support of $f$. We prove that two compact Hausdorff spaces are…

We present a necessary condition for a pair of $\mathcal{C}(K)$ spaces to be isomorphic in terms of topological properties of Cantor-Bendixon derivatives of $K$. This in particular gives a completely new information about the perfect…

We prove that there is a compact space $L$ and a 1-complemented subspace of the Banach space $C(L)$ which is not isomorphic to a space of continuous functions.