相关论文: A version of Kalton's theorem for the space of reg…

The following theorem is essentially due to L.~Kantorovich and B. Vulikh and it describes one of the most important classes of Banach lattices between which each continuous operator is regular. {\bf Theorem 1.1.} {\sl Let $E$ be an…

First we develop a technique to construct Banach lattices of homogeneous polynomials. We obtain, in particular, conditions for the linear spans of all positive compact and weakly compact $n$-homogeneous polynomials between the Banach…

Let $X$ and $E$ be $f$-algebras and $p:X \to E_+$ be a monotone vector norm. Then the triple $(X,p,E)$ is called a lattice-normed $f$-algebraic space. In this paper, we show a generalization of the extension of the Hahn-Banach theorem for…

Let $E, F$ be Archimedean Riesz spaces, and let $F^{\delta}$ denote an order completion of $F$. In this note, we provide necessary conditions under which the space of regular operators $\mathcal{L}^r(E, F)$ is pervasive in $\mathcal{L}^r(E,…

For a non-empty locally compact Hausdorff space $X$ and a Dedekind complete normal vector lattice $E$, we show that the vector lattice of norm to order bounded operators from ${\text C}_{\text c}(X)$ or ${\text C}_0(X)$ into $E$ is…

We show that the main problem left open in Wenzel: "Real and complex operator ideals" (wenzelopidls.latex), can be solved using the Banach spaces $Z_\alpha$ recently constructed by Kalton: "An elementary example of a Banach space not…

The aim of this article is to extend results of M.~Popov and second named author about orthogonally additive narrow operators on vector lattices. The main object of our investigations are an orthogonally additive narrow operators between…

Let $X$ and $Y$ be completely regular spaces and $E$ and $F$ be Hausdorff topological vector spaces. We call a linear map $T$ from a subspace of $C(X,E)$ into $C(Y,F)$ a \emph{Banach-Stone map} if it has the form $Tf(y) = S_{y}(f(h(y))$ for…

The paper alluded to in the title contains the following striking result: Let $I$ be the unit interval and $\Delta$ the Cantor set. If $X$ is a quasi Banach space containing no copy of $c_0$ which is isomorphic to a closed subspace of a…

Let $X$ and $Y$ be compact Hausdorff spaces, and $E$, $F$ be Banach lattices. Let $C(X,E)$ denote the Banach lattice of all continuous $E$-valued functions on $X$ equipped with the pointwise ordering and the sup norm. We prove that if there…

We introduce and study the enveloping norms of regularly P-operators between Banach lattices E and F, where P is a subspace of the space L(E,F) of continuous operators from E to F. We prove that if P is closed in L(E,F) in the operator norm…

In this paper we provide necessary and sufficient conditions for the existence of non-norm-attaining operators in $\mathcal{L}(E, F)$. By using a theorem due to Pfitzner on James boundaries, we show that if there exists a relatively compact…

An analogue of Kakutani's representation theorem for Banach lattice algebras is provided. We characterize Banach lattice algebras that embed as a closed sublattice-algebra of $C(K)$ precisely as those with a positive approximate identity…

It is shown that the regularly Lebesgue and regularly (quasi) KB operators in a Banach lattice E form operator algebras and, for Dedekind complete E, even Banach lattice algebras. We also prove that a Banach lattice E with order continuous…

In this paper we study the norm-attainment of positive operators between Banach lattices. By considering an absolute version of James boundaries, we prove that: If $E$ is a reflexive Banach lattice whose order is given by a basis and $F$ is…

By a result of Johnson, the Banach space $F=(\bigoplus_{n=1}^\infty \ell_1^n)_{\ell_\infty}$ contains a complemented copy of $\ell_1$. We identify $F$ with a complemented subspace of the space of (bounded, linear) operators on the reflexive…

Assume that a normed lattice $E$ is order dense majorizing of a vector lattice $E^t$. There is an extension norm $\Vert.\Vert_t$ for $E^t$ and we extend some lattice and topological properties of normed lattice $(E,\Vert.\Vert)$ to new…

Let $E$ and $F$ be Banach lattices. We show first that the disjointness preserving linear functionals separate the points of any infinite dimensional Banach lattice $E$, which shows that in this case the unbounded disjointness operators…

Given a Banach lattice $L,$ the space of lattice Lipschitz operators on $L$ has been introduced as a natural Lipschitz generalization of the linear notions of diagonal operator and multiplication operator on Banach function lattices. It is…

Let $E$, $F$ be separable Hilbert spaces, and assume that $E$ is infinite-dimensional. We show that for every continuous mapping $f:E\to F$ and every continuous function $\varepsilon: E\to (0, \infty)$ there exists a $C^{\infty}$ mapping…