On functions of negative type on the Olshanski spherical pair   $(SL(\infty),SU(\infty))$
  In this paper, using a generalized Bochner type representation for Olshanski spherical pairs, we prove the boundedness of every $SU(\infty)$-biinvariant continuous function of negative type on the infinite dimensional special linear group $SL(\infty)$. 
Marouane Rabaoui
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