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Paper   IPM / M / 17353
School of Mathematics
  Title:   Invariant means and multipliers on convolution quantum group algebras
  Author(s):  Mehdi Nemati (Joint with Ebrahimzadeh Esfahani and R. Esmailvandi)
  Status:   Published
  Journal: Int. J. Math.
  Year:  2023
  Pages:   DOI: 10.1142/S0129167X23500623
  Supported by:  IPM
Let ${\Bbb G}$ be a locally compact quantum group.Then the space $T(L^2({\Bbb G}))$ of trace class operators on $L^2({\Bbb G})$ is a Banach algebra with the convolution induced by the right fundamental unitary of ${\Bbb G}$. We show that properties of ${\Bbb G}$ such as amenability, triviality and compactness are equivalent to the existence of left or right invariant means on the convolution Banach algebra $T(L^2({\Bbb G}))$. We also investigate the relation between the existence of certain (weakly) compact right and left multipliers of $T(L^2({\Bbb G}))^{**}$ and some properties of ${\Bbb G}$.

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