Self-commutator inequalities in higher dimension

Abstract

Abstract. Three natural multi-dimensional substitutes for the self-commutator of a Hilbert space operator are introduced and generalizations of Putnam's inequality to tuples of operators with semidefinite self-commutators are indicated. In addition, a Riesz transform model is developed and investigated.

Algebra Environments I.

“…For more applications of algebra environments related to harmonic analysis and multivariable operator theory, we direct the attention of our reader to two groups of articles, Martin [36][37][38][39], and Martin [40][41][42][43]45], Martin, Salinas [50]. The list of specific issues includes Dirac operators with coefficients in a C *algebra, Cauchy-Pompeiu and Bochner-Martinelli-Koppelman representation formulas in a Banach algebra setting, maximal and fractional integral operators in Clifford analysis, generalizations of Ahlfors-Beurling and Alexander inequalities, quantitative Hartogs-Rosenthal theorems, Bochner-Weitzenböck and Bochner-Kodaira-Nakano self-commutator identities, extensions of Putnam inequality and singular integral models of seminormal systems of operators using Riesz transforms.…”