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 $A^*$?
The convergence of the adjoint operator
1
$\begingroup$
functional-analysis
convergence
operator-theory
adjoint-operators
-
0So you mean norm convergence? – 2012-12-09
-
0Yes I mean norm convergence – 2012-12-09
-
0Actually, an operator has the same norm as the norm of its adjoint. – 2012-12-09
-
0@DavideGiraudo Get it. – 2012-12-09