1:48 PM
I was thinking what I have left in this question?
0

The set of all adjoint operators are closed in Hilbert space. We are working with the operator norm. An operator $T$ is said to self-adjoint if $T = T^*$ where $T^*$ is the adjoint of operator $T$. To prove the above statement let us consider a sequence of adjoint operators $\{T_{n}\}$ conver...

Can you please clarify the question? What do you mean by "adjoint operator"? It looks like you are actually studying self-adjoint operators. Also, when you say closed, are you talking about operator norm topology? Are you working on a Banach space, Hilbert space, something else? — Nate Eldredge 12 mins ago
Yes,nice catch just did an edit! — BAYMAX 6 mins ago
@BAYMAX It seems that you still left adjoint in several places. Please, have a look whether my recent edits did not change what was your intended question.
To finish the proof, you probably want to use $\|S\|=\|S^*\|$ for $S=T-T_n$.

2:03 PM
Nice
I posted and did the edits
I missed self word many places though!
Welcome @AndresMejia!

thank you! just drifting by out of curiosity.

Nice!

2:26 PM
Welcome @ChilangoIncomprendido!

7 hours later…
9:21 PM
Is the convex hull of an arbitrary union the union of the convex hulls?