On the multiplicativity of linear operators

arXiv: Functional Analysis, 2020

In this survey, we shall present characterizations of some distinguished classes of Hilbertian bounded linear operators (namely, normal operators, selfadjoint operators, and unitary operators) in terms of operator inequalities related to the arithmetic-geometric mean inequality. For the class of all normal operators, we shall present new general characterizations.

Linear Algebra and its Applications, 2005

Journal of Fourier Analysis and Applications, 2018

We obtain new multilinear multiplier theorems for symbols of restricted smoothness which lie locally in certain Sobolev spaces. We provide applications concerning the boundedness of the commutators of Calderón and Calderón-Coifman-Journé. j∈Z (I − ∆) s/2 σ(2 j •) Ψ L 2 (R n) < ∞,

arXiv (Cornell University), 2015

Linear Algebra and its Applications, 1994

Porta, and Recht recently proved that (ISTS-' + S-'TSIj > 21jTI(. A generalization of this inequality to larger classes of operators and norms is obtained as an immediate consequence of the operator form of the arithmetic-geometric-mean inequality. Some related inequalities are also discussed. 1.

Journal of Inequalities and Applications, 2012

,B ∈ B(B(H)) denote either the generalized derivation δ A,B = L A -R B or the elementary operator A,B = L A R B -I, where L A and R B are the left and right multiplication operators defined on B(H) by L A = AX and R B = XB respectively. This article concerns some spectral properties of k-quasi- * -class A operators in a Hilbert space, as the property of being hereditarily polaroid. We also establish Weyl-type theorems for T and d A,B , where T is a k-quasi- * -class A operator and A, B * are also k-quasi- * -class A operators. MSC: Primary 47B47; 47A30; 47B20; secondary 47B10

Journal of Geometric Analysis, 2021

We present a short historical overview of the Miklhin-Hörmander and Marcinkiewicz multiplier theorems. We discuss different versions of them and provide comparisons. We also present a recent improvement of the Marcinkiewicz multiplier theorem in the two-dimensional case.

Acta Mathematica Hungarica, 1996

Journal of Functional Analysis, 2001

A multilinear version of Schur's test is obtained for products of L p spaces and is used to derive boundedness for multilinear multiplier operators acting on Sobolev and Besov spaces.

Crelle's Journal, 2012

In this paper, we provide a version of the Mihlin-Hörmander multiplier theorem for multilinear operators in the case where the target space is L p for p ≤ 1. This extends a recent result of Tomita [15] who proved an analogous result for p > 1.