A Banach algebra with an unbounded
A Banach algebra with an unbounded approximate identity.
******************************
Consider lp as a Banach algebra with coordinatewise operations. Let
en = (
(1,1,1,¼,1)
n |
,0,0,¼). Then
supn||en|| = sup{Ö[p]n ; n Î N} = ¥, and for every
x = (an) Î l2, limn||xen-x|| = limn(åk = n+1¥ |ak|p)[ 1/ p] = 0. Thus (en) is
required approximate identity.
File translated from
TEX
by
TTH,
version 2.70.
On 22 Feb 2001, 00:15.
|