Re: Shift operator in l^2

> 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?
.

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