TY - JOUR

T1 - Complete contractivity of maps associated with the Aluthge and Duggal transforms

AU - Foiaş, Ciprian

AU - Jung, Il Bong

AU - Ko, Eungil

AU - Pearcy, Carl

PY - 2003/4

Y1 - 2003/4

N2 - For an arbitrary operator T on Hilbert space, we study the maps Φ̃: f(T) → f(T̃) and Φ̂: f(T) → f(T̂), where T̃ and T̂are 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 T̂ and T̃, and also the inclusion W(f(T̃))- ∪ W(f(T̂))- ⊂ W(f(T))- relating the numerical ranges of f(T), f(T̃), and f(T̂).

AB - For an arbitrary operator T on Hilbert space, we study the maps Φ̃: f(T) → f(T̃) and Φ̂: f(T) → f(T̂), where T̃ and T̂are 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 T̂ and T̃, and also the inclusion W(f(T̃))- ∪ W(f(T̂))- ⊂ W(f(T))- relating the numerical ranges of f(T), f(T̃), and f(T̂).

UR - http://www.scopus.com/inward/record.url?scp=0038457460&partnerID=8YFLogxK

U2 - 10.2140/pjm.2003.209.249

DO - 10.2140/pjm.2003.209.249

M3 - Article

AN - SCOPUS:0038457460

SN - 0030-8730

VL - 209

SP - 249

EP - 259

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -