Vector-valued invariant means on spaces of bounded linear maps

• Autorzy: Mahshid Dashti , Rasoul Nasr-Isfahani , Sima Soltani Renani
• Języki publikacji: EN

Abstrakty

EN

Let 𝓐 be a Banach algebra and let ℳ be a W*-algebra. For a homomorphism Φ from 𝓐 into ℳ, we introduce and study ℳ -valued invariant Φ-means on the space of bounded linear maps from 𝓐 into ℳ. We establish several characterizations of existence of an ℳ -valued invariant Φ-mean on B(𝓐,ℳ). We also study the relation between existence of an ℳ -valued invariant Φ-mean on B(𝓐,ℳ) and amenability of 𝓐. Finally, for a character ϕ of 𝓐, we give some descriptions for ϕ-amenability of 𝓐 in terms of ℳ -valued invariant Φ-means.

Kategorie tematyczne

• 43A07: Means on groups, semigroups, etc.; amenable groups
• 46L10: General theory of von Neumann algebras
• 46H05: General theory of topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 132
• Numer: 1
• Strony: 1-11

Daty

wydano

2013

Twórcy

autor

Mahshid Dashti

• Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111 Isfahan, Iran
• Department of Mathematics, Malayer University, 65719-95863 Malayer, Hamedan, Iran

autor

Rasoul Nasr-Isfahani

• Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111 Isfahan, Iran
• School of Mathematics, Institute for Research, in Fundamental Science (IPM), 19395-5746 Tehran, Iran

autor

Sima Soltani Renani

• Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111 Isfahan, Iran

Identyfikatory

DOI

10.4064/cm132-1-1