Related papers: Commutators on $\ell_1$

What is the correct noncommutative generalization of the functor $C_0(X) \mapsto \ell^\infty(X)$ for locally compact Hausdorff $X$ having a countable basis? Making the ansatz $K(\ell^2) \mapsto B(\ell^2)$, we expect that every unital…

Let $\lambda$ be an infinite cardinal number and let $\ell_\infty^c(\lambda)$ denote the subspace of $\ell_\infty(\lambda)$ consisting of all functions that assume at most countably many non-zero values. We classify all infinite dimensional…

Given $1\leq q<p<\infty$ quantitative weighted L^p estimates, in terms of Aq weights, for vector valued maximal functions, Calder\'on-Zygmund operators, commutators and maximal rough singular integrals are obtained. The results for singular…

Using the extrapolation of one-sided weights, we establish the boundedness of commutators generated by weighted Lipschitz functions and one-sided singular integral operators from weighted Lebesgue spaces to weighted one-sided…

Let $F^{2,m}(\mathbb{C})$ denote the Fock-Sobolev space of complex plane. In this paper, we characterize the semi-commutator of two Toeplitz operators on $F^{2,m}(\mathbb{C})$ is zero. The result is different from the result of Bauer, Choe,…

In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.

We introduce and study a class of operator tuples in complex Hilbert spaces, which we call spherical tuples. In particular, we characterize spherical multi-shifts, and more generally, multiplication tuples on RKHS. We further use these…

We study the mapping property of the commutator of bilinear Hardy-Littlewood maximal operator in homogeneous Triebel-Lizorkin space. We also show that the commutator of bilinear Hardy-Littlewood maximal operator is a compact operator acting…

Let $H$ be a complex Hilbert space of dimension not less than $3$ and let ${\mathcal C}$ be a conjugacy class of compact self-adjoint operators on $H$. Suppose that the dimension of the kernels of operators from ${\mathcal C}$ not less than…

If $a,b$ are $n\times n$ matrices, Ando proved that Young's inequality is valid for their singular values: if $p>1$ and $1/p+1/q=1$, then $$ \lambda_k|ab^*|\le \lambda_k( \frac1p |a|^p+\frac 1q |b|^q ) \, \textit{ for all }k. $$ Later, this…

In \cite{CO-Tp-spaces}, the present authors initiated the study of composition operators on discrete analogue of generalized Hardy space $\mathbb{T}_{p}$ defined on a homogeneous rooted tree. In this article, we give equivalent conditions…

Denote by $T$ and $I_{\alpha}$ the bilinear Calder\'{o}n-Zygmund operators and bilinear fractional integrals, respectively. In this paper, it is proved that if $b_{1},b_{2}\in {\rm CMO}$ (the {\rm BMO}-closure of…

It is known that a continuous family of compact operators can be diagonalized pointwise. One can consider this fact as a possibility of diagonalization of the compact operators in Hilbert modules over a commutative W*-algebra. The aim of…

The aim of this paper is to get the boundedness of the commutators of multi-sublinear operators generated by local campanato functions and multilinear Calder\'on-Zygmund operators on the product generalized local Morrey spaces.

In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex…

We exhibit a singly generated, semisimple commutative operator algebra with a contractive approximate identity, such that the spectrum of the generator is a null sequence and zero, but the algebra is not the closed linear span of the…

In this paper, we prove that the null space of a weighted composition operator on $\ell_p~ (1 \leq p < \infty)$ is a complemented subspace. We also give a necessary and sufficient condition for a weighted composition operator on $\ell_p$…

We study first EP modular operators on Hilbert C*-modules and then we provide necessary and sufficient conditions for the product of two EP modular operators to be EP. These enable us to extend some results of Koliha [{\it Studia Math.}…

In this paper, the objects of our investigation are some dyadic operators, including dyadic shifts, multilinear paraproducts and multilinear Haar multipliers. We mainly focus on the continuity and compactness of these operators. First, we…

Unlike for $\ell_p$, $1<p\leq\infty$, the discrete Ces\`aro operator $C$ does not map $\ell_1$ into itself. We identify precisely those weights $w$ such that $C$ does map $\ell_1(w)$ continuously into itself. For these weights a complete…