Related papers: Martingale-like sequences in Banach lattices

Henstock-type integrals are considered, for functions defined in a Radon measure space and taking values in a Banach lattice X considering the norm and the order structure of the space. A number of results are obtained, highlighting the…

A subset of a Banach space is called equilateral if the distances between any two of its distinct elements are the same. It is proved that there exist non-separable Banach spaces (in fact of density continuum) with no infinite equilateral…

A banach space X is a normed vector space, which is complete with respect to the metric induced by the norm. Given a bounded linear operator T acting on a banach space X, T is said to attain its norm if there is a unit vector z in X, such…

This thesis presents a formalization of martingales in arbitrary Banach spaces using Isabelle/HOL. We begin by examining formalizations in prominent proof repositories and extend the definition of the conditional expectation operator from…

The essence of the notion of lineability and spaceability is to find linear structures in somewhat chaotic environments. The existing methods, in general, use \textit{ad hoc} arguments and few general techniques are known. Motivated by the…

A reflexive Banach space with an unconditional basis admits an equivalent $1$-unconditional $2R$ norm and embeds into a reflexive space with a $1$-symmetric $2R$ norm. Partial results on $1$-symmetric $2R$ renormings of spaces with a…

We prove the existence of free objects in certain subcategories of Banach lattices, including $p$-convex Banach lattices, Banach lattices with upper $p$-estimates, and AM-spaces. From this we immediately deduce that projectively universal…

First we adjust a technique due to Jim\'enez-Rodr\'iguez to prove the complete latticeability of the set of disjoint non-norm null weakly null sequences and of the set of disjoint non-norm null regular-polynomially null sequences in Banach…

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…

As a follow-up to a paper of D. Petz and J. Zem\'anek [4], a number of equivalent conditions which characterize the trace among linear functionals on matrix algebras, finite rank operators and the socle elements of semisimple Banach…

Using a multiplicative structure (for example that of a Banach algebra) and a partial order we construct a weak version of a Banach space valued stochastic integral with respect to square integrable martingales.

We characterize the order of principal congruences of a bounded lattice (also of a complete lattice and of a lattice of length 5) as a bounded ordered set. We also state a number of open problems in this new field.

The main purpose of this paper is to give a vector lattice version of a Theorem by Burkholder about convergence of martingales. The proof is based on a vector lattice analogue of Austin's sample function theorem, proved recently by Grobler,…

All most all the function spaces over real or complex domains and spaces of sequences, that arise in practice as examples of normed complete linear spaces (Banach spaces), are reflexive. These Banach spaces are dual to their respective…

We augment the dimension of the Euclidean space by one and the Picard iteration of a contraction by a simple iteration on the real line such that the resulting iteration becomes monotone increasing and bounded with respect to the order…

We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration…

We show that if a Banach lattice is projective, then every bounded sequence that can be mapped by a homomorphism onto the basis of $c_0$ must contain an $\ell_1$-subsequence. As a consequence, if Banach lattices $\ell_p$ or $FBL[E]$ are…

Given a Banach space $X$, we say that a sequence $\{x_n\}$ in the unit ball of $X$ is $L$-orthogonal if $\Vert x+x_n\Vert\rightarrow 1+\Vert x\Vert$ for every $x\in X$. On the other hand, an element $x^{**}$ in the bidual sphere is said to…

The subject of this work is to study martingales in a reductive homogeneous space with respect to a symmetric connection. Our basic idea is to view homogenous spaces as principal fiber bundles and, thus, to study martingales on homogeneous…

In this paper, we generalize the concept of unbounded norm (un) convergence: let $X$ be a normed lattice and $Y$ a vector lattice such that $X$ is an order dense ideal in $Y$; we say that a net $(y_\alpha)$ un-converges to $y$ in $Y$ with…