<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We establish directly factorization results for classes of ρ-contractions, corresponding to those obtained for certain classes of contractions. As an example of result which is not an immediate consequence of the fact that any ρ-contraction is similar to an ordinary contraction we give an "optimal" characterization of absolutely continuous ρ-contractions whose associated functional calculus has Property (A<sub>א₀</sub>). Along the way we show that a ρ-contraction is absolutely continuous if and only if it admits an absolutely continuous unitary ρ-dilation generalizing a well- known result for usual contractions. </p></abstract>

We establish directly factorization results for classes of ρ-contractions, corresponding to those obtained for certain classes of contractions. As an example of result which is not an immediate consequence of the fact that any ρ-contraction is similar to an ordinary contraction we give an "optimal" characterization of absolutely continuous ρ-contractions whose associated functional calculus has Property (Aא₀). Along the way we show that a ρ-contraction is absolutely continuous if and only if it admits an absolutely continuous unitary ρ-dilation generalizing a well- known result for usual contractions.

Factorizations in preduals associated to ρ-contractions

Department of Mathematics Université de Bordeaux Cours de la libération, 33405 Talence Cédex, FRANCE

Department of Mathematics Universitatea de Vest Timișoara, Bul. V. Pârvan nr. 4, 300232 Timișoara ROMANIA

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Factorizations in preduals associated to ρ-contractions"}

We establish directly factorization results for classes of ρ-contractions, corresponding to those obtained for certain classes of contractions. As an example...

Factorizations in preduals associated to ρ-contractions

Published Online: Dec 12, 2015

Page range: 3 - 17

Received: Jan 10, 2015

Accepted: Feb 28, 2015

DOI: https://doi.org/10.1515/awutm-2015-0001

Keywords
ρ-contraction, dilation, factorization, functional calculus

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Factorizations in preduals associated to ρ-contractions

Published Online: Dec 12, 2015

Page range: 3 - 17

Received: Jan 10, 2015

Accepted: Feb 28, 2015

DOI: https://doi.org/10.1515/awutm-2015-0001

Keywordsρ-contraction, dilation, factorization, functional calculus

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
ρ-contraction, dilation, factorization, functional calculus