Vector-valued invariant means on spaces of bounded linear maps

Mahshid Dashti ¹   ; Rasoul Nasr-Isfahani ²   ; Sima Soltani Renani ³

¹ Department of Mathematical Sciences Isfahan University of Technology 84156-83111 Isfahan, Iran and Department of Mathematics Malayer University 65719-95863 Malayer, Hamedan, Iran
² Department of Mathematical Sciences Isfahan University of Technology 84156-83111 Isfahan, Iran and School of Mathematics Institute for Research in Fundamental Science (IPM) 19395-5746 Tehran, Iran
³ Department of Mathematical Sciences Isfahan University of Technology 84156-83111 Isfahan, Iran

Colloquium Mathematicum, Tome 132 (2013) no. 1, pp. 1-11

Résumé

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.

Détail

DOI : 10.4064/cm132-1-1

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