Re: Finite rank linear operator

From: Robin Chapman (rjc_at_ivorynospamtower.freeserve.co.uk)
Date: 09/21/04 

Date: Tue, 21 Sep 2004 09:20:31 +0100

Alexander Korovyev wrote:

> Suppose X is a Hilbert space and L is a linear operator. If L(X) is
> finite dimensional does it follow that L is bounded?

No, there are unbounded linear functionals from any infinite-dimensional
Hilbert space to R (or C if you prefer complex Hilbert spaces). 

-- 
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
"Lacan, Jacques, 79, 91-92; mistakes his penis for a square root, 88-9"
Francis Wheen, _How Mumbo-Jumbo Conquered the World_