Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I am considering a linear map $T:X^\*\to Y^\*$ where $X^\*$ and $Y^\*$ are dual Banach spaces. I would like to know if I can deduce that $T$ is weak* continuous (I consider the weak* topologies on both $X^\*$ and $Y^\*$) if I know either of the following: [1] $T$ is weak* continuous when restricted to the unit ball of $X^\*$; [2] for any integer $n$, $T$ is weak* continuous when restricted to the ball $B(0; n)$ in $X^\*$.

in my case neither $X$ nor $Y$ is reflexive.

share|cite|improve this question

1 Answer 1

up vote 4 down vote accepted

Yes. From the Krein Smulian theorem (use Google) you get that $T^*$ maps $Y$ into $X$.

share|cite|improve this answer

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.