Related papers: A remark on non-commutative $L^p$-spaces

The algebra of functions on kappa-Minkowski noncommutative spacetime is studied as algebra of operators on Hilbert spaces. The representations of this algebra are constructed and classified. This new approach leads to a natural construction…

The study of operator algebras on Hilbert spaces, and C*-algebras in particular, is one of the most active areas within Functional Analysis. A natural generalization of these is to replace Hilbert spaces (which are $L^2$-spaces) with…

Some identities for noncommutative perspectives of operator monotone functions in Hilbert spaces aregiven. Applications for weighted operator geometric mean and relative operator entropy are also provided.

Let $M$ be a von Neumann algebra, let $\varphi$ be a normal faithful state on $M$ and let $L^p(M,\varphi)$ be the associated Haagerup non-commutative $L^p$-spaces, for $1\leq p\leq\infty$. Let $D\in L^1(M,\varphi)$ be the density of…

Let $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra, equipped with a normal faithful state $\varphi$, and let $\mathcal{A}$ be a maximal subdiagonal subalgebra of $\mathcal{M}$. We have proved that for $0< p<1$, $H^p(\mathcal{A})$ is…

Let $L$ be a linear operator on $L^2(\mathbb R^n)$ generating an analytic semigroup $\{e^{-tL}\}_{t\ge0}$ with kernels having pointwise upper bounds and $p(\cdot):\ \mathbb R^n\to(0,1]$ be a variable exponent function satisfying the…

We describe a new operator space structure on $L_p$ when $p$ is an even integer and compare it with the one introduced in our previous work using complex interpolation. For the new structure, the Khintchine inequalities and Burkholder's…

Given a strictly increasing sequence $\Lambda=(\lambda_n)$ of nonegative real numbers, with $\sum_{n=1}^\infty \frac{1}{\lambda_n}<\infty$, the M\"untz spaces $M_\Lambda^p$ are defined as the closure in $L^p([0,1])$ of the monomials…

Let $\mathcal{M}$ be a von Neumann algebra equipped with a normal semifinite faithful trace, $(\mathbb{X},\,d,\,\mu)$ be a space of homogeneous type in the sense of Coifman and Weiss, and…

Several examples and models based on noncommutative differential calculi on commutative algebras indicate that a metric should be regarded as an element of the left-linear tensor product of the space of 1-forms with itself. We show how the…

An analogue of the Lehmann-Symanzik-Zimmermann reduction formula is obtained for the case of noncommutative space-space theory. Some consequences of the reduction formula and Haag's theorem are discussed.

In this paper, we first introduce a quantum $n$-space with a cocommutative Hopf algebra structure. Then it is shown that to this quantum $n$-space there corresponds a derivation algebra of $\sigma$-twisted derivations related to some…

In the present paper we introduce a certain class of non commutative Orlicz spaces, associated with arbitrary faithful normal locally-finite weights on a semi-finite von Neumann algebra $M.$ We describe the dual spaces for such Orlicz…

In the present paper we continue our study of non-commutative operator graphs in infinite-dimensional spaces. We consider examples of the non-commutative operator graphs generated by resolutions of identity corresponding to the…

We study the description of semicommutative Hardy spaces in terms of molecules. We use this characterization to obtain $\mathrm{H}_1^c - \mathrm{H}_1^c$ estimates for Calder\'on-Zygmund operators with kernels with values in a semifinite von…

Let $\vec{p}\in(0,\infty)^n$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. In this article, via the non-tangential grand maximal function, the authors first introduce the anisotropic mixed-norm Hardy spaces…

In analogy with the maximal tensor product of $C^*$-algebras, we define the ``maximal" tensor product $E_1\otimes_\mu E_2$ of two operator spaces $E_1$ and $E_2$ and we show that it can be identified completely isometrically with the sum of…

In this paper we extend previous results of Banach, Lamperti and Yeadon on isometries of Lp-spaces to the non-tracial case first introduced by Haagerup. Specifically, we use operator space techniques and an extrapolation argument to prove…

We develop a $GL_{qp}(2)$ invariant differential calculus on a two-dimensional noncommutative quantum space. Here the co-ordinate space for the exterior quantum plane is spanned by the differentials that are commutative (bosonic) in nature.

Non-commutative $L^p$-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For $p\geq 2$ they are also proved to possess a {\em sufficient} family of bounded positive sesquilinear forms…