Related papers: (E,F)-multipliers and applications

Given a finite subset S in F_p^d, let a(S) be the number of distinct r-tuples (x_1,...,x_r) in S such that x_1+...+x_r = 0. We consider the "moments" F(m,n) = sum_|S|=n a(S)^m. Specifically, we present an explicit formula for F(m,n) as a…

Let $P_{\alpha} f(x,t)$ be the Caffarelli-Silvestre extension of a smooth function $f(x): \mathbb{R}^n \rightarrow \mathbb{R}^{n+1}_+:=\mathbb{R}^n\times (0,\infty).$ The purpose of this article is twofold. Firstly, we want to characterize…

We prove several versions of Grothendieck's Theorem for completely bounded linear maps $T\colon E \to F^*$, when E and F are operator spaces. We prove that if E,F are $C^*$-algebras, of which at least one is exact, then every completely…

Let $G$ be a semisimple Lie group, ${\frak g}$ its Lie algebra. For any symmetric space $M$ over $G$ we construct a new (deformed) multiplication in the space $A$ of smooth functions on $M$. This multiplication is invariant under the action…

We study multiplier theorems on a vector-valued function space, which is a generalization of the results of Calder\'on-Torchinsky and Grafakos-He-Honz\'ik-Nguyen, and an improvement of the result of Triebel. For $0<p<\infty$ and $0<q\leq…

We prove multiplier theorems on rank one noncompact symmetric spaces which improve aspects of existing results. A common theme of our main results is that we partially drop specific assumptions on the multiplier function such as a…

This is a survey of the current state of the theory of $F$--(super)manifolds $(M,\circ)$, first defined in [HeMa] and further developed in [He], [Ma2], [Me1]. Here $\circ$ is an $\Cal{O}_M$--bilinear multiplication on the tangent sheaf…

We prove that the sequence space $\ell_{p,q}$ does not embed into $L_{p,q}(\mathcal{M},\tau)$ for any noncommutative probability space $(\mathcal{M},\tau)$, $1< p<\infty $, $1\le q<\infty$, $p\ne q$. Several applications to the isomorphic…

In the main result of the paper we extend Rosenthal's characterization of Banach spaces with the Schur property by showing that for a quasi-complete locally convex space $E$ whose separable bounded sets are metrizable the following…

We give conditions for when two Euler products are the same given that they satisfy a functional equation and their coefficients are not too large and do not differ from each other by too much. Additionally, we prove a number of…

In this paper we consider equimeasurable symmetric(rearrangement invariant) spaces $\mathbf{E}_1 = \mathbf{E}_1(\Omega_1,\mathcal{F}_1,\mu_1)$ and $\mathbf{E}_2 = \mathbf{E}_2(\Omega_2,\mathcal{F}_2,\mu_2)$ on a measure spaces $(\Omega_1,…

We provide sequence space representations for the test function space $\mathcal{D}_{E}$ and the distribution space $\mathcal{D}^{\prime}_{E}$ associated to a Banach space $E$ belonging to a broad class of translation-modulation invariant…

Letting $E$, $F$ be Banach spaces, the main two results of this paper are the following: (1) If every (linear bounded) operator $E\rightarrow F$ is unconditionally converging, then every polynomial from $E$ to $F$ is unconditionally…

We investigate a Grothendieck-type inequality for pairs of Banach spaces $E,F$ assuming $E$ is finite-dimensional and study the associated Grothendieck-type constant. We prove that if there is a $C >0$ such that $\|A\otimes…

It is quite an interesting phenomenon in Topology that configuration spaces on a manifold M are intrinsically related to certain mapping spaces from M. In this paper we interpret and greatly expand on this relationship. Building (mainly) on…

We introduce a new family $\mathcal{A}_{n,k}$ of Schur positive symmetric functions, which are defined as sums over totally symmetric plane partitions. In the first part, we show that, for $k=1$, this family is equal to a multivariate…

Starting from Jacobi-Trudi's type determinental expressions for the Schur functions corresponding to types $B,C$ and $D,$ we define a natural $q$-analogue of the multiplicity $[V(\lambda):M(\mu)]$ when $M(\mu)$ is a tensor product of row or…

We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue-Orlicz spaces of a discrete group and relative Toeplitz-Schur multipliers on Schatten-von-Neumann-Orlicz classes. Four applications are given:…

We provide quite sufficient conditions on the Banach spaces $E$ and $F$ in order to obtain the spaceability of the set of all linear operators from $E$ into $F$ which are $q$-compact but not $p$-compact. Also, under similar conditions over…

Every compact symmetric space $M$ admits a dual noncompact symmetric space $\check{M}$. When $M$ is a generalized Grassmannian, we can view $\check{M}$ as a open submanifold of it consisting of space-like subspaces \cite{HL}. Motivated from…