Tensor algebras, displacement structure, and the Schur algorithm

The positive Schur property on positive projective tensor products and spaces of regular multilinear operators

We characterize the positive Schur property in the positive projective tensor products of Banach lattices, we establish the connection with the weak operator topology and we give necessary and sufficient conditions for the space of regular multilinear operators/homogeneous polynomials taking values in a Dedekind complete Banach lattice to have the positive Schur property.

Haagerup张量积与Schur乘子

Haagerup tensor products and Schur multipliers

本文比较多类Schur乘子，证明关于测度与谱测度的Schur乘子和对应$L^\infty$空间的Haagerup张量积等距重合，该结论由离散Schur乘子的已知类似结果推导得出。

On a tensor-analogue of the Schur product

We consider the tensorial Schur product $R \circ^\otimes S = [r_{ij} \otimes s_{ij}]$ for $R \in M_n(\mathcal{A}), S\in M_n(\mathcal{B}),$ with $\mathcal{A}, \mathcal{B}$ unital $C^*$-algebras, verify that such a `tensorial Schur product' of positive operators is again positive, and then use this fact to prove (an apparently marginally more general version of) the classical result of Choi that a linear map $ϕ:M_n \to M_d$ is completely positive if and only if $[ϕ(E_{ij})] \in M_n(M_d)^+$, where of course $\{E_{ij}:1 \leq i,j \leq n\}$ denotes the usual system of matrix units in $M_n (:= M_n(\m…

Tensor Algebras and Displacement Structure. III. Asymptotic properties

We continue to investigate some classes of Szegö type polynomials in several variables. We focus on asymptotic properties of these polynomials and we extend several classical results of G. Szegö to this setting.

Tensor algebras and displacement structure. II. Noncommutative Szego polynomials

In this paper we continue to explore the connection between tensor algebras and displacement structure. We focus on recursive orthonormalization and we develop an analogue of the Szego type theory of orthogonal polynomials in the unit circle for several noncommuting variables. Thus, we obtain the recurrence equations and Christoffel-Darboux type formulas, as well as a Favard type result. Also we continue to study a Szego kernel for the N-dimnesional unit ball of an infinite dimensional Hilbert space.

Schur multipliers of Schatten--von Neumann classes $\boldsymbol{S_p}$

We study in this paper properties of Schur multipliers of Schatten von Neumann classes $\boldsymbol{S}_p$. We prove that for $p\le1$, Schur multipliers of $\boldsymbol{S}_p$ are necessarily completely bounded. We also introduce for $p\le1$ a scale ${\mathscr W}_p$ of tensor products of $\ell^\infty$ and prove that matrices in ${\mathscr W}_p$ are Schur multipliers of $\boldsymbol{S}_p$. We compare this sufficient condition with the sufficient condition of membership in the $p$-tensor product of $\ell^\infty$ spaces.