Misra, Gadadhar ; Narasimha Sastry, N. S. (1990) Homogeneous tuples of operators and holomorphic discrete series representation of some classical groups Journal of Operator Theory, 24 (1). pp. 2332. ISSN 03794024

PDF
 Publisher Version
337kB 
Official URL: http://www.theta.ro/jot/archive/1990024001/1990...
Abstract
Let T = (T_{1}....., T_{n}) be a ntuple of bounded linear operators on a fixed Hilbert space . H and let φ be a biholomorphic automorphism of Ω, the joint spectrum of T. In this paper, we consider those ntuples T for which the joint spectrum Ω is of the form G/K, a bounded symmetric domain. Let φ be any biholornorphic automorphism of the domain Ω. Define, phi(T) via a suit able functional calculus and call a ntuple of operators T homogeneous if φ(T) .is simultaneously unitarily equivalent to T for every automorphism φ of Ω. For each homogeneous operator T, let U_{φ} be a unitary] operator implimenting this equivalence. We obtain a characterisation of all the homogeneous operators CowenDouglas class and show that it is possible to choose the unitary U_{φ} in such a way that the map φ→ U_{φ} 1 is a unitary representation of the group of of biholomorpic automorphisms of Ω.
Item Type:  Article 

Source:  Copyright of this article belongs to The Theta Foundation. 
ID Code:  67112 
Deposited On:  28 Oct 2011 10:29 
Last Modified:  18 May 2016 14:22 
Repository Staff Only: item control page