Vector-valued invariant means on spaces of bounded linear maps
Colloquium Mathematicum, Tome 132 (2013) no. 1, pp. 1-11
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let ${\mathcal A}$ be a Banach algebra and let ${\mathcal M}$ be a $W^*$-algebra. For a homomorphism $\varPhi $ from ${\mathcal A}$ into ${\mathcal M}$, we introduce and study ${\mathcal M}$-valued invariant $\varPhi $-means on the space of bounded linear maps from ${\mathcal A}$ into ${\mathcal M}$. We establish several characterizations of existence of an ${\mathcal M}$-valued invariant $\varPhi $-mean on $B({\mathcal A},{\mathcal M})$. We also study the relation between existence of an ${\mathcal M}$-valued invariant $\varPhi $-mean on $B({\mathcal A},{\mathcal M})$ and amenability of ${\mathcal A}$. Finally, for a character $\phi $ of ${\mathcal A}$, we give some descriptions for $\phi $-amenability of $\mathcal A$ in terms of ${\mathcal M}$-valued invariant $\varPhi $-means.
Keywords:
mathcal banach algebra mathcal * algebra homomorphism varphi mathcal mathcal introduce study mathcal valued invariant varphi means space bounded linear maps mathcal mathcal establish several characterizations existence mathcal valued invariant varphi mean mathcal mathcal study relation between existence mathcal valued invariant varphi mean mathcal mathcal amenability mathcal finally character phi mathcal descriptions phi amenability mathcal terms mathcal valued invariant varphi means
Affiliations des auteurs :
Mahshid Dashti 1 ; Rasoul Nasr-Isfahani 2 ; Sima Soltani Renani 3
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author = {Mahshid Dashti and Rasoul Nasr-Isfahani and Sima Soltani Renani},
title = {Vector-valued invariant means on spaces of bounded linear maps},
journal = {Colloquium Mathematicum},
pages = {1--11},
publisher = {mathdoc},
volume = {132},
number = {1},
year = {2013},
doi = {10.4064/cm132-1-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm132-1-1/}
}
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Mahshid Dashti; Rasoul Nasr-Isfahani; Sima Soltani Renani. Vector-valued invariant means on spaces of bounded linear maps. Colloquium Mathematicum, Tome 132 (2013) no. 1, pp. 1-11. doi: 10.4064/cm132-1-1
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