Homogeneous Operators, Jet Construction and Similarity

Abstract

In this paper we show, starting with the jet construction, how to construct all the irreducible homogeneous operators in the Cowen-Douglas class B n (D) whose associated representations are multiplicity-free.

A family of homogeneous operators in the Cowen–Douglas class over the poly-disc

“…A bounded linear operator T on a complex separable Hilbert space H is said to be homogeneous if its spectrum σ(T ) is contained in D and g(T ) is unitarily equivalent to T for every g in the Möbius group Möb. Indeed, since g ∈ Möb is a rational function with pole outside D, it follows that g(T ) is well defined whenever σ(T ) ⊂ D. In a number of articles [1,2,6,7,9,12], the class of homogeneous operators has been studied extensively.…”