Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If a sequence of operator $A_n$ converges in norm to $A$, i.e. $\lim \lVert A_n-A\rVert=0$)where $A_n$ and $A\in B(H)$ ($H$ is the Hilbert space). Is it true that $A_n^*$ converges in norm to $A^*$?

share|cite|improve this question
So you mean norm convergence? – JSchlather Dec 9 '12 at 20:25
Yes I mean norm convergence – 89085731 Dec 9 '12 at 20:25
Actually, an operator has the same norm as the norm of its adjoint. – Davide Giraudo Dec 9 '12 at 20:34
@DavideGiraudo Get it. – 89085731 Dec 9 '12 at 20:41

Since $(A_n-A)^*=A_n^*-A^*$ and an operator has the same norm with the adjoint operator,so $||A_n-A||=||A_n^*-A^*||$,then we get the answer.

share|cite|improve this answer
The step "an operator has the same norm as its adjoint" deserves more details. – Davide Giraudo Dec 9 '12 at 20:55

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.