Schatten class and Berezin transform of quaternionic linear operators. (28th July 2016)

• Record Type: Journal Article
• Authors: Colombo, Fabrizio; Gantner, Jonathan; Janssens, Tim
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 18(2016:Dec. 15)
• Page Start: 5582
• Page End: 5606
• Publication Date: 2016-07-28
• Subjects: Schatten class of operators -- spectral theorem and the S‐spectrum -- Berezin transform of quaternionic operators -- weighted Bergman spaces of slice hyperholomorphic functions; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3944
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we introduce the Schatten class and the Berezin transform of quaternionic operators. The first topic is of great importance in operator theory, but it is also necessary to study the second one, which requires the notion of trace class operators, a particular case of the Schatten class. Regarding the Berezin transform, we give the general definition and properties. Then we concentrate on the setting of weighted Bergman spaces of slice hyperholomorphic functions. Our results are based on the S ‐spectrum of quaternionic operators, which is the notion of spectrum that appears in the quaternionic version of the spectral theorem and in the quaternionic S ‐functional calculus. Copyright © 2016 John Wiley & Sons, Ltd.