Mathematica Eterna
Open Access

Abstract

Composition-operator-preserving maps

Nizar JAOUA

For a given space X of holomorphic functions in the open unit disc, we determine which self-maps Φ of L(X) preserve the family FC(X) of composition operators leaving X invariant. We show that their surjective multiplicative restrictions to FC(X) are exactly of the form Φ(T) = A−1T A with A a bijective member of FC(X). We characterize the normpreserving ones by the same form with A induced by a rotation. We generalize these results to the semi-multiplicative maps.

Published Date: 2018-09-05;