Related papers: Operator synthesis and tensor products

Using techniques from TRO equivalence of masa bimodules we prove various transference results: We show that when $\alpha$ is a group homomorphism which pushes forward the Haar measure of $G$ to a measure absolutely continuous with respect…

We investigate the orthogonality preserving property for pairs of mappings on inner product $C^*$-modules extending existing results for a single orthogonality-preserving mapping. Guided by the point of view that the $C^*$-valued inner…

In this paper, we consider bivariate Cheney-Sharma operators which are not the tensor product construction. Precisely, we show that these operators preserve Lipschitz condition of a given Lipschitz continuous function f and also the…

Let $B(X)$ be the Banach algebra of all bounded linear operators acting on a Banach space $X$. Are sums and products of commuting decomposable operators on Banach spaces decomposable? This is one of the most important open problems in the…

Let $(\mathcal G, \Sigma)$ be an ordered abelian group with Haar measure $\mu$, let $(\mathcal A, \mathcal G, \alpha)$ be a dynamical system and let $\mathcal A\rtimes_{\alpha} \Sigma $ be the associated semicrossed product. Using Takai…

In this paper we prove that if S equals a finite sum of finite products of Toeplitz operators on the Bergman space of the unit disk, then S is compact if and only if the Berezin transform of S equals 0 on the boundary of the disk. This…

Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous frames for tensor product of Hilbert spaces. This includes, for example,…

In this paper we introduce the crossed product construction for a discrete group action on an operator system. In analogy to the work of E. Katsoulis and C. Ramsey, we describe three canonical crossed products arising from such a dynamical…

In this work we consider the $\eta$-invariant for pseudodifferential operators of tensor product type, also called bisingular pseudodifferential operators. We study complex powers of classical bisingular operators. We prove the trace…

A Banach space operator $T\in B(X)$ is left polaroid if for each $\lambda\in\hbox{iso}\sigma_a(T)$ there is an integer $d(\lambda)$ such that asc $(T-\lambda)=d(\lambda)<\infty$ and $(T-\lambda)^{d(\lambda)+1}X$ is closed; $T$ is finitely…

We show that in a finite tensor category, the tensor product property holds for support varieties if and only if it holds between indecomposable periodic objects. We apply this to certain Hopf algebras in the form of skew group algebras. In…

We develop the compactness theory of multilinear singular integrals on product spaces using a modern point of view. The first main result is a compact $T1$ theorem for multilinear Calder\'{o}n--Zygmund operators on product spaces. More…

Let $C_\varphi$ be a composition operator acting on the Hardy space of the unit disc $H^p$ ($1\leq p < \infty$), which is embedded in a $C_0$-semigroup of composition operators $\mathcal{T}=(C_{\varphi_t})_{t\geq 0}.$ We investigate whether…

Let $\Omega\subset \mathbb{C}^n$ for $n\geq 2$ be a bounded pseudoconvex domain with a $C^2$-smooth boundary. We study the compactness of composition operators on the Bergman spaces of smoothly bounded convex domains. We give a partial…

Let H be a complex Hilbert space, B(H) and S(H) be the spaces of all bounded operators and all self-adjoint operators on H, respectively. We give the concrete forms of the maps on B(H) and also S(H) which preserve the spectrum of certain…

In this paper, we consider the boundedness properties of multilinear $\theta$-type Calder\'on--Zygmund operators $T_\theta$ recently introduced in the literature. First, we prove strong type and weak type estimates for multilinear…

Let $ G $ be a locally compact group. We study the categories of $ L^{\infty}(G) $-comodules and $ L(G) $-comodules in the setting of dual operator spaces and the associated crossed products. It is proved that every $ L^{\infty}(G)…

We obtain sufficient and necessary conditions on weight functions $s_1(t),\ldots,s_m(t)$ and $\psi(t)$ so that the weighted multilinear Hardy-Ces\`{a}ro operator \[(f_1,\ldots,f_m)\mapsto \int_{[0,1]^n}\left(\prod_{k=1}^nf_k\left(s_k(t)…

We study unital operator spaces endowed with a partially defined product. We give a matrix-norm characterization of such products that allows for a representation theorem where the partial product is realized as composition of operators on…

The operator product expansion is used to compute the matrix elements of composite renormalized operators on the lattice. We study the product of two fundamental fields in the two-dimensional sigma-model and discuss the possible sources of…