Re: Shift operator in l^2

> In article
> <12403523.1114791352332.JavaMail.jakarta@xxxxxxxxxxxxx
> forum.org>,
> Valeriu Anisiu <vanisiu@xxxxxxxxxxx> wrote:
> >> In article
> >>
> <15013082.1114784188237.JavaMail.jakarta@xxxxxxxxxxxxx
> >> forum.org>,
> >> Valeriu Anisiu <vanisiu@xxxxxxxxxxx> wrote:
> >>
> >> > Let S be the (left) shift operator in l^2(C),
> >> > S(x_1,x_2,...) = (x_2,x_3,...).
> >> > For e>0 does there exist an invertible operator
> T
> >> > such that ||S-T|| < e ?.
> >> >
> >> > Thank you,
> >> >
> >> > V. Anisiu
> >>
> >> Show that if T is invertible and ||S-T|| < ||S||,
> >> then T is invertible.
>
> >I beg your pardon?
>
> I think he meant to say that if ||S-T|| < 1, T maps
> the subspace
> {x: x_1 = 0} onto l^2.
>
> Robert Israel
> israel@xxxxxxxxxxx
> Department of Mathematics
> http://www.math.ubc.ca/~israel
> University of British Columbia Vancouver,
> BC, Canada


This is true but does not solve the problem.

V. Anisiu
.

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