Equivalent norms question

Hi,

suppose || || is a norm in an infinite dimensional vector space V.
Suppose that 1 <= c < infinity is given. What requirements must || ||
fulfill for there to be an inner product norm ||| ||| over V with the
(equivalency) property:

1/c*||x|| <= |||x||| <= c*||x||, for all x in V ?

Regards,

-Kasimir Blomstedt

.