Related papers: Some remarks on noncommutative Khintchine inequali…
Let $X_1, X_2,\dots$ be a short-memory linear process of random variables. For $1\leq q<2$, let $\cF$ be a bounded set of real-valued functions on $[0,1]$ with finite $q$-variation. It is proved that…
We extend some results of Kwok-Pun Ho. In particular, it will be shown that every rearrangement-invariant quasi-Banach function space E on a totally sigma-finite measure space with a non-atomic measure can be expressed is the form…
We show that for a sequence in a Banach space, the property of being stable under large perturbations characterizes the property of being equivalent to the unit vector basis of $l_1$. We show that a normalized unconditional basic sequence…
We prove maximal inequalities for $L_q$-valued martingales obtained by stochastic integration with respect to compensated random measures. A version of these estimates for integrals with respect to compensated Poisson random measures were…
We show that a positive operator between $L^p$-spaces is given by integration against a kernel function if and only if the image of each positive function has a lower semi-continuous representative with respect to a suitable topology. This…
These notes have the intent to introduce the study of the nonlinear aspects of operator space theory. We investigate some results on the nonlinear theory of Banach spaces which remain valid in the noncommutative case. In particular, we show…
In this work we aim to analyze the Clauser-Horne-Shimony-Holt CHSH inequality strictly in the context of probability theory. In the course of assembling inequality we have to take care not to produce assumptions a priori, that is,…
We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of…
Let $X, Y$ be two independent identically distributed (i.i.d.) random variables taking values from a separable Banach space $(\mathcal{X}, \|\cdot\|)$. Given two measurable subsets $F, K\subseteq\cal{X}$, we established distribution free…
We present moment inequalities for completely degenerate Banach space valued (generalized) U-statistics of arbitrary order. The estimates involve suprema of empirical processes which, in the real-valued case, can be replaced by simpler…
We study a class of quasi-variational inequality problems defined over infinite dimensional Banach space and deduce sufficient conditions for ensuring solutions to such problems under the upper semi-continuity and pseudomonotonicity…
We establish some linear and nonlinear integral inequalities of Gronwall-Bellman-Bihari type for functions with two independent variables on general time scales. The results are illustrated with examples, obtained by fixing the time scales…
In this paper, we consider a product of a symmetric stable process in $\mathbb{R}^d$ and a one-dimensional Brownian motion in $\mathbb{R}^+$. Then we define a class of harmonic functions with respect to this product process. We show that…
We study properties of continuous semi-homogeneous operators of degree $k$ via various functions (e.g. measures of noncompactness) on all bounded subsets of a Banach space. We prove necessary and sufficient conditions for these functions to…
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…
In this paper we introduce the notion of slice regular right linear semigroup in a quaternionic Banach space. It is an operatorial function which is slice regular (a noncommutative counterpart of analyticity) and which satisfies a…
This note is devoted to several results about frequency localized functions and associated Bernstein inequalities for higher order operators. In particular, we construct some counterexamples for the frequency-localized Bernstein…
Matrix concentration inequalities give bounds for the spectral-norm deviation of a random matrix from its expected value. These results have a weak dimensional dependence that is sometimes, but not always, necessary. This paper identifies…
Let $A$ be an unbounded operator on a Banach space $X$. It is sometimes useful to improve the operator $A$ by extending it to an operator $B$ on a larger Banach space $Y$ with smaller spectrum. It would be preferable to do this with some…
If T is a bounded linear operator acting on an infinite-dimensional Banach space, then there exists and operator F of rank at most one and arbitrarily small norm such that T-F has an invariant subspace of infinite dimension and codimension.…