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Let $G$ be locally compact group. How we can show that $$ M(C_0(G)\otimes C_b(G))=C_b(G,C_b(G)). $$ ($M(C_0(G)\otimes C_b(G))$ is the multiplier algebra of $C_0(G)\otimes C_b(G)$)

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Which part can't you show? (Also, the fact $G$ is a group seems to play no role in what you want to prove.) – Yemon Choi May 29 '13 at 1:18
I do not know how to define a bijection between them. – zzzz May 29 '13 at 6:37
I can define a map from $_M(C0(G) \otimes C_b(G))$ to $C_b(G,C_b(G))$ but I can not show that the map is sujective. by the way, you are right, I do not need to assume $G$ is a group. – zzzz May 29 '13 at 6:42
Try defining a map that goes the other way from right hand side to left hand side? – Yemon Choi May 29 '13 at 16:02
yes but I couldnt – zzzz May 30 '13 at 0:41

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