Related papers: Non-commutative Khintchine type inequalities assoc…

We consider two operator space versions of type and cotype, namely $S_p$-type, $S_q$-cotype and type $(p,H)$, cotype $(q,H)$ for a homogeneous Hilbertian operator space $H$ and $1\leq p \leq 2 \leq q\leq \infty$, generalizing "$OH$-cotype…

In \cite{jpsf} we constructed pairs of units $u,v$ in $\Z$-orders of a quaternion algebra over $\Q (\sqrt{-d})$, $d \equiv 7 \pmod 8$ positive and square free, such that $< u^ n,v^n>$ is free for some $n\in \mathbb{N}$. Here we extend this…

We consider the algebra of invariants of $d$-tuples of $n\times n$ matrices under the action of the orthogonal group by simultaneous conjugation over an infinite field of characteristic $p$ different from two. It is well-known that this…

We characterize classes of linear maps between operator spaces $E$, $F$ which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative $L^p$ spaces $S_p[E^*]$ based on the Schatten classes on the…

This work will be centered in commutative Banach subalgebras of the algebra of bounded linear operators defined on a Free Banach spaces of countable type. The main goal of this work wil be to formulate a representation theorem for these…

In this paper, we study the boundedness, compactness and Schatten class membership of composition operators on the weighted $L^{p}$-space of a tree $L^{p}_{\lambda}(T)$ with $1\leq p <\infty$.

Let $p\in [1,\infty)$. We define an $L^p$-operator algebra crossed product by a transfer operator for the topological Bernoulli shift $\varphi$ on $X=\{1,...,n\}^{\mathbb{N}}$, and we prove it is isometrically isomorphic to the $L^p$-analog…

We establish Calder\'on-type theorems for operators bounded on nonstandard end-point Lorentz spaces \begin{equation*} T\colon L^{p_0, q_0}\to L^{p_1, q_1}\quad\text{and}\quad T\colon L^{q, 1}\to L^\infty \end{equation*} and the improvement…

For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…

On a compact connected group $G$, consider the infinitesimal generator $-L$ of a central symmetric Gaussian convolution semigroup $(\mu_t)_{t>0}$. We establish several regularity results of the solution to the Poisson equation $LU=F$, both…

Our aim in this article is to contribute to the theory of Lipschitz free $p$-spaces for $0<p\le 1$ over the Euclidean spaces $\mathbb{R}^d$ and $\mathbb{Z}^d$. To that end, on one hand we show that $\mathcal{F}_p(\mathbb{R}^d)$ admits a…

This paper focuses on the cohomology of operator algebras associated with the free semigroup generated by the set $\{z_{\alpha}\}_{\alpha\in\Lambda}$, with the left regular free semigroup algebra $\mathfrak{L}_{\Lambda}$ and the…

Let $\Gamma$ be a torsion-free arithmetic group acting on its associated global symmetric space $X$. Assume that $X$ is of non-compact type and let $\Gamma$ act on the geodesic boundary $\partial X$ of $X$. Via general constructions in…

A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with…

Let $\mathcal{M}$ be a semifinite von Neumann algebra and let $E$ be a symmetric function space on $(0,\infty)$. Denote by $E(\mathcal{M})$ the non-commutative symmetric space of measurable operators affiliated with $\mathcal{M}$ and…

In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality…

In this paper we prove that several operator algebras are completely isomorphic to each other; e.g., the $C^*_\lambda(F_k)$, $k\geq 2$, the $C^*$-algebras generated by the regular left representation $\lambda:F_k\to B(\ell_2(F_k))$, are…

We prove scalar and operator-valued Khintchine inequalities for mixtures of free and tensor-independent semicircle variables, interpolating between classical and free Khintchine-type inequalities. Specifically, we characterize the norm of…

We investigate the norm of sums of independent vector-valued random variables in noncommutative Lp spaces. This allows us to obtain a uniform family of complete embeddings of the Schatten class Sq^n in Sp(lq^m) with optimal order m = n^2.…

We show that there is an operator space notion of Lipschitz embeddability between operator spaces which is strictly weaker than its linear counterpart but which is still strong enough to impose linear restrictions on operator space…