Re: linear algebra, inner product spaces

In article <46360c52$0$17951$4fafbaef@xxxxxxxxxxxxxxxxxxx>,
Kiuhnm <"kiuhnm03["@]yahoo.it> wrote:
Let V be a complex inner product space and T a self-adjoint linear
operator on V.
I must show that I+iT is non-singular.
I have proven that it is injective, but I have trouble with surjectivity.
My idea was to show that for each v in V there exists w in V s.t.
||w+iTw - v|| = 0, exploiting the identity (Ta|b) = (a|Tb).

Kiuhnm

Can you prove that I + T^2 is non-singular? If so, you can
write down the inverse. Or you can use the spectral decomposition
of T.

I presume that T is bounded, or T is not defined everywhere.
However, (I+iT)^-1 is a normal operator defined everywhere.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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