Related papers: Noncommutative $L_p$-space and operator system
Let 1 \le p < q \le 2 and let M be any von Neumann algebra. We use recent techniques from free harmonic analysis to construct a completely isomorphic embedding of Lq(M) (equipped with its natural operator space structure) into Lp(A) for…
We prove noncommutative Khintchine inequalities for all interpolation spaces between $L_p$ and $L_2$ with $p<2$. In particular, it follows that Khintchine inequalities hold in $L_{1,\infty}$. Using a similar method, we find a new…
We define norms on $L_p(\mathcal{M}) \otimes M_n$ where $\mathcal{M}$ is a von Neumann algebra and $M_n$ is the complex $n \times n$ matrices. We show that a linear map $T: L_p(\mathcal{M}) \to L_q(\mathcal{N})$ is decomposable if…
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 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…
The following theorem is the main result of this note. Theorem 1. Let $(E, \|\cdot\|_E) $ be a rearrangement invariant Banach function space on the interval $[0, 1]$. If $E$ is isometric to $\L_p [0, 1]$ for some $1\le p<\infty$, then $E$…
Continuing the study initiated in our earlier article [7], this paper aims to characterize various continuity properties of nonlinear composition operators acting on some sequence spaces, giving special attention to the space of sequences…
Let $\cal M$ be a semi-finite von Neumann algebra equipped with a distinguished faithful, normal, semi-finite trace $\tau$. We introduce the notion of equi-integrability in non-commutative spaces and show that if a rearrangement invariant…
We show that a reflexive subspace of the predual of a von Neumann algebra embeds into a noncommutative Lp space for some p>1. This is a noncommutative version of Rosenthal's result for commutative Lp spaces. Similarly for 1 < q < 2, an…
Let $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra, equipped with a normal faithful state $\varphi$, and let $\mathcal{A}$ be maximal subdiagonal subalgebra of $\mathcal{M}$ and $1\le p<\8$. We prove a Beurling-Blecher-Labuschagne…
We introduce and systematically develop the theory of \emph{quantum doubly stochastic operators}, i.e. positive, trace-preserving maps on non-commutative $L_p$-spaces associated to semifinite von Neumann algebras. After establishing basic…
We demonstrate new abstract characterizations for unital and non-unital operator spaces. We characterize unital operator spaces in terms of the cone of accretive operators (operators whose real part is positive). Defining the gauge of an…
We give an alternate proof of one of the inequalities proved recently for martingales (=sums of martingale differences) in a non-commutative $L_p$-space, with $1<p<\infty$, by Q. Xu and the author. This new approach is restricted to $p$ an…
We study large linear structures inside sets arising in the theory of norm-attaining operators. We provide several results in the context of lineability, spaceability, maximal-spaceability, and $(\alpha, \beta)$-spaceability for sets of…
Boundedness and compactness properties of multiplication operators on quantum (non-commutative) function spaces are investigated. For endomorphic multiplication operators these properties can be characterized in the setting of quantum…
We give a proof of the Khintchine inequalities in non-commutative $L_p$-spaces for all $0< p<1$. These new inequalities are valid for the Rademacher functions or Gaussian random variables, but also for more general sequences, e.g. for the…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
By using graded (super) Lie algebras, we can construct noncommutative superspace on curved homogeneous manifolds. In this paper, we take a flat limit to obtain flat noncommutative superspace. We particularly consider $d=2$ and $d=4$…
We find a class of algebras A satisfying the following property: for every nontrivial noncommutative polynomial, the linear span of all its values in A equals A. This class includes the algebras of all bounded and all compact operators on…
Elliptic and parabolic integro-differential model problems are considered in the whole space. By verifying H\"ormander condition, the existence and uniqueness is proved in L_{p}-spaces of functions whose regularity is defined by a scalable,…