Prove the adjoint property of operator sum

[danja347]

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

$$\tilde{(\hat{A} + <br /> \hat{B})^*} = <br /> \tilde{\hat{A}}^* + <br /> \tilde{\hat{B}}^*$$

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

 

[dextercioby]

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

$$\tilde{(\hat{A} + <br /> \hat{B})^*} = <br /> \tilde{\hat{A}}^* + <br /> \tilde{\hat{B}}^*$$

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

Explain what everything means:tilda stands for what?star stands for what?hats stand for what??
P.S.I had my glasses on,so i could read it.

 

[arildno]

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

 

[marlon]

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

regards
marlon

 

[dextercioby]

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

regards
marlon

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.

 

[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 can't just say that the operators are linear and write the answer down.

Please... some advice!