Class A composition operators on H-2

Abstract

In this paper, we study class A composition operators C-phi on the Hardy space H-2. We show that if C-phi belongs to class A, then 0 is a fixed point of the symbol phi As a corollary, we obtain that every invertible class A composition operator is unitary. Moreover, we examine spectral properties and the commutants of class A composition operators. We also prove that if phi is a linear fractional self-map of ID into itself, then C-phi belongs to class A if and only if it is subnormal. Finally, we provide some conditions under which C-phi* belongs to class A. (C) 2015 Elsevier Inc. All rights reserved.