## spectral measure of multiplication operator [closed]

hi,

i have the following question: let $(X,\mu)$ be a finite measure space and consider the operator $T : L^{2}(X, \mu) \rightarrow L^{2}(X, \mu)$ given by $Tf(x) = \varphi(x) f(x)$, where $\varphi : X \rightarrow \mathbb{R}$ is a bounded measurabel function. Is there any possibility to determine the spectral measure? hope this question is not too trivial. thanks in advance.

beno

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I know the results for the position operator, but is there any possibility to figure it out in general ? – beno Jan 12 2012 at 14:29
Obviously it is $\varphi \cdot \mu$. You should ask your question at math.stackexchange.com – Kofi Jan 12 2012 at 14:53
how can one see this ? – beno Jan 12 2012 at 15:15
MathOverflow is for research level questions. This is just basic spectral theory for bounded linear operators. The appropriate place to ask this question is posted above. Also any book on functional analysis answers this question. – Kofi Jan 12 2012 at 15:20
Following Kofi's suggestion, this has since been posted at math.stackexchange.com/questions/98480/… where it is receiving answers. – Yemon Choi Jan 12 2012 at 22:32