Related papers: 2-positive contractive projections on noncommutati…

In 1969 Lindenstrauss and Rosenthal showed that if a Banach space is isomorphic to a complemented subspace of an L_p-space, then it is either a script L_p-space or isomorphic to a Hilbert space. This is the motivation of this paper where we…

We investigate the isometric structure of $L^{p}$-spaces for the infinite-dimensional Lebesgue measure $(\mathbb{R}^{\mathbb{N}},\mu)$. Under the continuum hypothesis (CH) we prove $L^{p}(\mu)\cong \ell^{p}(\mathfrak{c},L^{p}[0,1])$, where…

Building on the theory of noncommutative complex structures, the notion of a noncommutative K\"ahler structure is introduced. In the quantum homogeneous space case many of the fundamental results of classical K\"ahler geometry are shown to…

Let $L$ be a finite-dimensional non-abelian Lie algebra with the center $Z(L)$. In this paper, we define a non-commuting graph associated with $L$ as the graph whose vertex set is the projective space of the quotient algebra $L/Z(L)$, and…

For each value of $p$ such that $0<p<1$, we give a specific example of two functions in the Hardy space $H^p$ and in the Bergman space $A^p$ that do not satisfy the triangle inequality. For Hardy spaces, this provides a much simpler proof…

We describe absolutely ordered $p$-normed spaces, for $1 \le p \le \infty$ which presents a model for "non-commutative" vector lattices and includes order theoretic orthogonality. To demonstrate its relevance, we introduce the notion of…

Suppose $0 < p \leq 2$ and that $(\Omega, \mu)$ is a measure space for which $L_{p}(\Omega, \mu)$ is at least two-dimensional. The central results of this paper provide a complete description of the subsets of $L_{p}(\Omega, \mu)$ that have…

This paper focuses on systems of strongly coupled elliptic operators whose coefficients may be unbounded and are defined on a domain $\Omega \subseteq \mathbb{R}^d$. It is shown that a quasi-contractive semigroup in $L^p$-spaces can be…

We prove optimal estimates for the mapping properties of the Bergman projection on the Hartogs triangle in weighted $L^p$ spaces when $p>\frac{4}{3}$, where the weight is a power of the distance to the singular boundary point. For…

We consider convolution equations of the type f * T = g where f, g are in L^p(R^n) and T is a compactly supported distribution. Under natural assumptions on the zero set of the Fourier transform of T we show that f is compactly supported,…

Let A be a C*-algebra and A** its enveloping von Neumann algebra. C. Akemann suggested a kind of non-commutative topology in which certain projections in A** play the role of open sets. The adjectives "open", "closed", "compact", and…

Let T : Lp --> Lp be a contraction, with p strictly between 1 and infinity, and assume that T is analytic, that is, there exists a constant K such that n\norm{T^n-T^{n-1}} < K for any positive integer n. Under the assumption that T is…

We consider a large class of geodesic metric spaces, including Banach spaces, hyperbolic spaces and geodesic $\mathrm{CAT}(\kappa)$-spaces, and investigate the space of nonexpansive mappings on either a convex or a star-shaped subset in…

We obtain $L^p$ regularity for the Bergman projection on some Reinhardt domains. We start with a bounded initial domain $\Omega$ with some symmetry properties and generate successor domains in higher {dimensions}. We prove: If the Bergman…

For a fixed $1\le p<+\infty$ denote by $\Vert\cdot\Vert_p$ the usual norm in the space $l_p$ (or $L_p$). In this paper we prove that for all real numbers $p$ and $q$ such that $2\le p\le q$ holds $$ 2(\Vert x\Vert_p^q+\Vert y\Vert_p^q)\le…

This article contains two rigidity type results for $\mathrm{SL}(n,\mathbb{Z})$ for large $n$ that share the same proof. Firstly, we prove that for every $p \in [1,\infty]$ different from $2$, the noncommutative $L^p$-space associated with…

We consider second-order elliptic equations in a half space with leading coefficients measurable in a tangential direction. We prove the $W^2_p$-estimate and solvability for the Dirichlet problem when $p\in (1,2]$, and for the Neumann…

In this paper, we establish dimension-free $L_p$-estimates for operator-valued maximal spherical means over cyclic groups $\Z_{m+1}^d$ for all $p>1$ and $m\geq1$. The key ingredient is a noncommutative extension of the spectral technique…

We define embedding of an $n$-dimensional normed space into $L_{-p},\ 0<p<n$ by extending analytically with respect to $p$ the corresponding property of the classical $L_p$-spaces. The well-known connection between embeddings into $L_p$ and…

This paper is devoted to the study of Hermite operators acting on noncommutative $L_{p}$-spaces. In the first part, we establish the noncommutative maximal inequalities for Bochner-Riesz means associated with Hermite operators and then…