Vector-valued invariant means on spaces of bounded linear maps

Tom 132 / 2013

Mahshid Dashti, Rasoul Nasr-Isfahani, Sima Soltani Renani Colloquium Mathematicum 132 (2013), 1-11 MSC: 46H05, 43A07, 46L10. DOI: 10.4064/cm132-1-1

Streszczenie

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.

Autorzy

  • Mahshid DashtiDepartment of Mathematical Sciences
    Isfahan University of Technology
    84156-83111 Isfahan, Iran
    and
    Department of Mathematics
    Malayer University
    65719-95863 Malayer, Hamedan, Iran
    e-mail
  • Rasoul Nasr-IsfahaniDepartment 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
    e-mail
  • Sima Soltani RenaniDepartment of Mathematical Sciences
    Isfahan University of Technology
    84156-83111 Isfahan, Iran
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek