Is it true?

From: twiki (twikiNO13SPAM_at_libero.it)
Date: 10/09/04 

Date: Sat, 09 Oct 2004 15:51:36 GMT

if ||.||2 is euclidean norm and ||.|| generic matricial-norm then

(1) ||A||2 = inf ||A|| forall ||.|| ???

i've the proof of this inequality

rho(A)<=||A|| forall submultiplicative matricial-norm

(rho(A)=spectral radius of A)

the (1) equation is true if A is symmetric matrix.
For generic A this i've the confused notes for (1).
My notes on (1) inequality make use of jordan-decomposition of A
and (2) inequality for to proof that J=X^(-1)AX is symmetrizable
with *arbitrary precision* ???

if you have the suggestions or link for the (1) please help me!!!
thanks

(grace for my terrible english!!!)