Related papers: On the Generalized Difference Matrix Domain on Str…

We discuss a new pseudometric on the space of all norms on a finite-dimensional vector space (or free module) $\mathbb{F}^k$, with $\mathbb{F}$ the real, complex, or quaternion numbers. This metric arises from the Lipschitz-equivalence of…

The Bayesian perspective on inverse problems has attracted much mathematical attention in recent years. Particular attention has been paid to Bayesian inverse problems (BIPs) in which the parameter to be inferred lies in an…

Let $\mathscr{C}_n=\{-1,1\}^n$ be the discrete hypercube equipped with the uniform probability measure $\sigma_n$. Talagrand's influence inequality (1994) asserts that there exists $C\in(0,\infty)$ such that for every $n\in\mathbb{N}$,…

We consider the closed subspace of $\ell_\infty$ generated by $c_0$ and the characteristic functions of elements of an uncountable, almost disjoint family $\mathcal A$ of infinite subsets of $\mathbb N$. This Banach space has the form…

The notion of a strongly summing sequence is introduced. Such a sequence is weak-Cauchy, a basis for its closed linear span, and has the crucial property that the dual of this span is not weakly sequentially complete. The main result is:…

We study Banach envelopes for commutative symmetric sequence or function spaces, and noncommutative symmetric spaces of measurable operators. We characterize the class $(HC)$ of quasi-normed symmetric sequence or function spaces $E$ for…

Let $B(E,F)$ denote the set of all bounded linear operators from $E$ into $F$, and $B^+(E,F)$ the set of double splitting operators in $B(E,F)$. When both $E,F$ are infinite dimensional , in $B(E,F)$ there are not more elementary…

The problem of describing the range of a Bergman space B_2(G) under the Cauchy transform K for a Jordan domain G was solved by Napalkov (Jr) and Yulmukhametov. It turned out that K(B_2(G))=B_2^1(C\bar G) if and only if G is a quasidisk;…

A subsequence principle is obtained, characterizing Banach spaces containing $c_0$, in the spirit of the author's 1974 characterization of Banach spaces containing $\ell^1$. Definition: A sequence $(b_j)$ in a Banach space is called {\it…

The aim of the paper is to introduced the spaces $c_{0}^{\lambda}(\hat{F})$ and $c^{\lambda}(\hat{F})$ which are the BK-spaces of non-absolute type and also derive some inclusion relations. Further, we determine the…

Let C be a nonempty closed convex subset of a real normed linear space $E$ and u, v are positive numbers. In this paper we introduce some new definitions that generalize the analogue definitions from real Hilbert spaces to real normed…

The main results of the paper: {\bf (1)} The dual Banach space $X^*$ contains a linear subspace $A\subset X^*$ such that the set $A^{(1)}$ of all limits of weak$^*$ convergent bounded nets in $A$ is a proper norm-dense subset of $X^*$ if…

In this paper we establish some new results concerning the Cauchy-Peano problem in Banach spaces. Firstly, we prove that if a Banach space $E$ admits a fundamental biorthogonal system, then there exists a continuous vector field $f\colon…

Let $({\cal X},\|\:.\:\|)$ be a Banach space. In general, for a $C_0$-semigroup \semi on $({\cal X},\|\:.\:\|)$, its adjoint semigroup \semia is no longer strongly continuous on the dual space $({\cal X}^{*},\|\:.\:\|^{*})$. Consider on…

We prove Bernstein-type matrix concentration inequalities for linear combinations with matrix coefficients of binary random variables satisfying certain $\ell_\infty$-independence assumptions, complementing recent results by Kaufman, Kyng…

Consider a nonlinear ill-posed operator equation $F(u)=y$ where $F$ is defined on a Banach space $X$. In general, for solving this equation numerically, a finite dimensional approximation of $X$ and an approximation of $F$ are required.…

We introduce and study multivariate generalizations of the classical BV spaces of Jordan, F. Riesz and Wiener. The family of the introduced spaces contains or is intimately related to a considerable class of function spaces of modern…

Our basic element is a $C^1$ mapping $f:X\to Y$, with $X,Y$ Banach spaces, and with derivative everywhere invertible. So $f$ is a local diffeomorphism at every point. The aim of this paper is to find a sufficient condition for $f$ to be…

We study the notions of acs, luacs and uacs Banach spaces which were introduced by V. Kadets et al. in 2000 and form common generalisations of the usual rotundity and smoothness properties of Banach spaces. In particular, we are interested…

A map f between two metric spaces (X,d_1) and (Y,d_2) is called a coarse embedding of X into Y if there exist two nondecreasing functions phi_1, phi_2:[0,\infty) --> [0,\infty) such that: phi_1(d_1(x,y)) \leq d_2(f(x),f(y)) \leq…