Analysis seminar

Parasar Mohandy, Indian Institute of Technology

"Space of completely bounded Lp multipliers and its pre-dual"

Let G be a locally compact group. G. Pisier considered the operator space
structure (oss) on L^p(G) by developing operator space complex interpolation. In this oss one can define completely bounded L^p(G) multipliers. It is natural to ask whether the space of completely bounded multipliers on L^p(G) denoted by M^cb_p (G) is strictly contained inside M_p(G), the space of multipliers on L^p(G). For p = 1 and 2 it can be shown that these two spaces coincide. In this talk we will see that M^cb_p (G) ( M_p(G) for any infinite locally compact abelian group G. In the process one can get the cb version of Herz's multiplier homomorphism theorem.
It is well known that pre-dual of M_p(G) can be identified with Figa-Talamanca-Herz algebra A_p(G). We will address the question of pre-dual of M^cb_p (G).