Related papers: L-embedded Banach spaces and measure topology
Let $\cal M$ be a semi-finite von Neumann algebra equipped with a distinguished faithful, normal, semi-finite trace $\tau$. We introduce the notion of equi-integrability in non-commutative spaces and show that if a rearrangement invariant…
In this book we study metric and topological versions of projectivity injectivity and flatness of Banach modules over Banach algebras. These two non-standard versions of Banach homology theories are studied in parallel under unified…
The paper deals with the study of Banach spaces whose duals are injective Banach lattices. Davies in 1967 proved that an ordered Banach space is an $L^1$-predual space if and only if it is a simplex space. In 2007 Duan and Lin proved that a…
This paper is devoted to introduce a topology on BL-algebras, makes them semitopological algebras. For any BL-algebra $\mathcal{L}=(L, \wedge, \vee, *, \to , 0, 1)$, the introduced topology is defined by a distance-like function between…
In the article is introduced a new class of Banach spaces that are called sub B-convex. Namely, a Banach space X is said to be B -convex if it may be represented as a direct sum l_1+ W, where W is B-convex. It will be shown that any…
It is shown that every continuous homomorphism of Arens-Michael algebras can be obtained as the limit of a morphism of certain projective systems consisting of Fr\'{e}chet algebras. Based on this we prove that a complemented subalgebra of…
The regular open subsets of a topological space form a Boolean algebra, where the `join' of two regular open sets is the interior of the closure of their union. A `credence' is a finitely additive probability measure on this Boolean…
We show that complemented subspaces of uncountable products of Banach spaces are products of complemented subspaces of countable subproducts.
In this paper, we study the coarse embedding into Banach space. We proved that under certain conditions, the property of embedding into Banach space can be preserved under taking the union the metric spaces. For a group $G$ strongly…
We introduce the Integrated Dual Local Depth which is a local depth measure for data in a Banach space based on the use of one-dimensional projections. The properties of a depth measure are analyzed under this setting and a proper…
We introduce a family of Banach spaces of measures, each containing the set of measures with density of bounded variation. These spaces are suitable for the study of weighted transfer operators of piecewise-smooth maps of the interval where…
We study the structure of the space of coarse Lipschitz maps between Banach spaces. In particular we introduce the notion of norm attaining coarse Lipschitz maps. We extend to the case of norm attaining coarse Lipschitz equivalences, a…
We study some aspects of countably additive vector measures with values in $\ell_\infty$ and the Banach lattices of real-valued functions that are integrable with respect to such a vector measure. On the one hand, we prove that if $W…
We present an isometric version of the complementably universal Banach space $\mathcal{B}$ with a monotone Schauder basis. The space $\mathcal{B}$ is isomorphic to Pe{\l}czy\'nski's space with a universal basis as well as to Kadec'…
In this paper, the notion of semi-compact perturbation of a closed linear subspace is introduced. Then for a of pair of closed linear subspace of a Banach space such that one is a semi-compact perturbation of the other, it is proved that…
In this paper we construct an injection from the linear space of trigonometric polynomials defined on $\mathbb{T}^d$ with bounded degrees with respect to each variable to a suitable linear subspace $L^1_E\subset L^1(\mathbb{T})$. We give…
We introduce the concept of topological radical of a Banach module. This closed submodule have two description: the as the intersection of ranges of maximal contractive monomorphism (from outside) and as the union of ranges of small…
We construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any compact and convex subset is continuous but not uniformly continuous. The space we construct is locally…
We characterize the relatively compact subsets of $L^1\left(\| m \| \right),$ the quasi-Banach function space associated to the semivariation of a given vector measure $m$ showing that the strong connection between compactness, uniform…
Banach algebra A for which the natural embedding x into x^ of A into WAP(A)* is bounded below; that is, for some m in R with m > 0 we have ||x^|| > m ||x||, is called a WAP-algebra. Through we mainly concern with weighted measure algebra…