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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-1,
author = {Mahshid Dashti and Rasoul Nasr-Isfahani and Sima Soltani Renani},
title = {Vector-valued invariant means on spaces of bounded linear maps},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {1-11},
zbl = {1293.46027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-1}
}
Mahshid Dashti; Rasoul Nasr-Isfahani; Sima Soltani Renani. Vector-valued invariant means on spaces of bounded linear maps. Colloquium Mathematicae, Tome 131 (2013) pp. 1-11. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-1/