Gleason's problem and Schur multipliers in the multivariable quaternionic setting

Abstract

We define and study the counterparts of Gleason's problem, of the Drury–Arveson's space and of Schur multipliers when the unit ball of CN is replaced by the unit ball of HN, where H denotes the algebra of real quaternions. Schur multipliers are characterized in terms of coisometric operator matrices in quaternionic spaces. Finally, we define the counterpart of Blaschke factors in this setting and study a one point interpolation problem.