Complete contractivity of maps associated with the Aluthge and Duggal transforms

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

Research output: Contribution to journalArticlepeer-review

36 Scopus citations

Abstract

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).

Original languageEnglish
Pages (from-to)249-259
Number of pages11
JournalPacific Journal of Mathematics
Volume209
Issue number2
DOIs
StatePublished - Apr 2003

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