Re: 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


This is the problem of isomorphic characterization of Hilbert spaces.
The most famous result is due to Lindenstrauss and Tzafriri:
a Banach space is isomorphic to a Hilbert space
iff every closed subspace is complemented.

V. Anisiu
.

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