# 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.