Vector-valued invariant means on spaces of bounded linear maps

Mahshid Dashti, Rasoul Nasr-Isfahani, and Sima Soltani Renani. "Vector-valued invariant means on spaces of bounded linear maps." Colloquium Mathematicae 132.1 (2013): 1-11. <http://eudml.org/doc/283444>.

@article{MahshidDashti2013,
abstract = {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.},
author = {Mahshid Dashti, Rasoul Nasr-Isfahani, Sima Soltani Renani},
journal = {Colloquium Mathematicae},
keywords = {Banach algebra; vector-valued invariant mean; -amenability; -algebra},
language = {eng},
number = {1},
pages = {1-11},
title = {Vector-valued invariant means on spaces of bounded linear maps},
url = {http://eudml.org/doc/283444},
volume = {132},
year = {2013},
}

TY - JOUR
AU - Mahshid Dashti
AU - Rasoul Nasr-Isfahani
AU - Sima Soltani Renani
TI - Vector-valued invariant means on spaces of bounded linear maps
JO - Colloquium Mathematicae
PY - 2013
VL - 132
IS - 1
SP - 1
EP - 11
AB - 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.
LA - eng
KW - Banach algebra; vector-valued invariant mean; -amenability; -algebra
UR - http://eudml.org/doc/283444
ER -