Related papers: Remarks on the non-commutative Khintchine inequali…

The Kahane--Salem--Zygmund inequality for multilinear forms in $\ell_{\infty}$ spaces claims that, for all positive integers $m,n_{1},...,n_{m}$, there exists an $m$-linear form $A\colon\ell_{\infty}^{n_{1}}\times\cdots\times…

We define 2-indexed $(q,p)$-Schatten quasi-norms for any $q,p > 0$ on operators on a tensor product of Hilbert spaces, naturally extending the norms defined by Pisier's theory of operator-valued Schatten spaces. We establish several…

Let T:=[T_1,..., T_n] be an n-tuple of operators on a Hilbert space such that T is a completely non-coisometric row contraction. We establish the existence of a "one-to-one" correspondence between the joint invariant subspaces under…

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…

We investigate a rearrangement inequality for pairs of n-square matrices: Let |A\|_p denote the C^p trace norm of an n-square matrix A. Consider the quantity |A+B|_p^p + |A-B|_p^p. Under certain positivity conditions, we show that this is…

It has been shown in "On the Hausdorff-Young theorem for commutative hypergroups" by Sina Degenfeld-Schonburg, that one can extend the domain of Fourier transform of a commutative hypergroup $K$ to $L^p(K)$ for $1\leq p \leq 2$, and the…

In [18] we have shown that, for $p_{1},p_{2}\in(2,\infty]$, the constants of Bennett's inequality on unimodular bilinear forms on $\ell_{p_{1}}^{n_{1} }\times\ell_{p_{2}}^{n_{2}}$ are asymptotically bounded by $1$. In the present paper we…

We study the nonlinear Schr\"odinger equation for systems of $N$ orthonormal functions. We prove the existence of ground states for all $N$ when the exponent $p$ of the non linearity is not too large, and for an infinite sequence $N_j$…

Given a Radon measure $\mu$ on $R^d$, which may be non doubling, we introduce a space of type BMO with respect to this measure. It is shown that many properties that hold when $\mu$ is doubling remain valid for the space BMO introduced in…

We prove a noncommutative $(p,p)$-Poincar\'e inequality for trace-symmetric quantum Markov semigroups on tracial von Neumann algebras, assuming only the existence of a spectral gap. Extending semi-commutative results of Huang and Tropp, our…

In this work, the $L_p$ version (for $p> 1$) of the dimensional Brunn-Minkowski inequality for the standard Gaussian measure $\gamma_n(\cdot)$ on $\mathbb{R}^n$ is shown. More precisely, we prove that for any $0$-symmetric convex sets with…

In this article we obtain some positive results about the existence of a common nontrivial invariant subspace for $N$-tuples of not necessarily commuting operators on Banach spaces with a Schauder basis. The concept of joint quasinilpotence…

In this paper, we establish the quantitative mean ergodic theorems for two subclasses of power bounded operators on a fixed noncommutative $L_p$-space with $1<p<\infty$, which mainly concerns power bounded invertible operators and Lamperti…

Let $\BS_1,...,\BS_n$ be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter $p\in(0,1)$. Let $m_*(p):=(1+p+2p^2)/(2\sqrt{p-p^2}+4p^2)$ if $0<p\le 1/2$ and $m_*(p):=1$ if…

In this paper we study in a Hilbert space a homogeneous linear second order difference equation with nonconstant and noncommuting operator coefficients. We build its exact resolutive formula consisting in the explicit non-iterative…

This paper is devoted to the study of noncommutative weak Orlicz spaces and martingale inequalities. Marcinkiewicz interpolation theorem is extended to include noncommutative weak Orlicz spaces as interpolation classes. In particular, we…

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…

For $1\leq q \leq n-2$, we provide explicit examples to demonstrate non-compactness of the Neumann operator for the Kohn Laplacian acting on $L^2$ $(0,q)$-forms on the unit ball in $(2n+1)$-dimensional Heisenberg space.

We prove continuity properties of higher order commutators of fractional operators on the multilinear setting, between a product of weighted Lebesgue spaces into certain weighted Lipschitz spaces. The considered operators include the…

This paper is a follow-up contribution to our work [20] where we discussed some invariant subspace results for contractions on Hilbert spaces. Here we extend the results of [20] to the context of n-tuples of bounded linear operators on…