Complete contractivity of maps associated with the Aluthge and Duggal transforms

Ciprian Foiaş, Il Bong Jung, Eungil Ko and Carl Pearcy

Vol. 209 (2003), No. 2, 249–259

DOI: 10.2140/pjm.2003.209.249

Abstract

For an arbitrary operator T on Hilbert space, we study the maps Φ : f(T) → f(T) and Φ : f(T) → f(T), where T and T are the Aluthge and Duggal transforms of T, respectively, and f belongs to the algebra Hol(σ(T)). We show that both maps are (contractive and) completely contractive algebra homomorphisms. As applications we obtain that every spectral set for T is also a spectral set for T and T, and also the inclusion W(f(T))⁻∪ W(f(T))⁻⊂ W(f(T))⁻ relating the numerical ranges of f(T), f(T), and f(T).

Milestones

Received: 4 April 2002

Published: 1 April 2003