Algebraic Problem

1. Nov 29, 2004

danja347

I need help proving this equation... Thankful for all answers!

$$\tilde{(\hat{A} + \hat{B})^*} = \tilde{\hat{A}}^* + \tilde{\hat{B}}^*$$

I hope you can read my nice Latex equation! :)

2. Nov 29, 2004

dextercioby

Explain what everything means:tilda stands for what?star stands for what?hats stand for what??

3. Nov 29, 2004

arildno

I would assume it is about (complex) conjugates and transposes, but I'm not sure..

4. Nov 29, 2004

marlon

at think the same thing arildno...and since these operations are per definition linear there is not much to say...

regards
marlon

5. Nov 29, 2004

dextercioby

The problem is not that simple.In general,linear operators can be bounded/unbounded.So the general formula reads.
$$(\hat{A} +\hat{B})^{+} \supseteq \hat{A}^{+}+\hat{B}^{+}$$
,where the sign for operator equality stands for bounded linear operators A and B.

6. Nov 29, 2004

danja347

My latex knowledge ís not that good... but dextercioby wrote my problem down for me except that there is an equality sign in my problem! What i want to do is to prove equality. I cant just say that the operators are linear and write the answer down.