Let $V$ be a reflexive banach space. If $W$ is a Banach space and if $T$ is in $L(V,W)$, show that $T(B)$ is closed in $W$ where $B$ is closed unit ball in $V$, the problem is in the chapter of weak and weak$^{\ast}$ topologies but I am not getting any hint what result I should use. please help.
Closedness of the image of the closed unit ball under a linear operator from a reflexive Banach space to an arbitrary Banach space
2
$\begingroup$
functional-analysis
banach-spaces
-
3You wrote that $T$ is a reflexive Banach space, but $T$ is the operator. Is it $V$ or $W$ that should be reflexive? Also, your questions will be easier to read and get more attention if you use complete sentences and correct grammar and punctuation. – 2011-04-13