New posts in Functional Analysis

$X'$ finite-dimensional implies $X$ finite-dimensional

Norm and Weak Topologies agree?

Convergence in $C([0,T_0],L^2)$ and uniform boundedness in $C([0,T_0],H^2)$ gives convergence in $C([0,T_0],H^1)$.

Is a Hahn-Banach extension always continuous?

Prove that if $f(x)=f(y)$ for all $f\in X^{*},$ then $x=y$

Compact subset of space of Continuous functions

Funky function-composed within itself umpteen thousand times

Integral Operator in $L^2$

What is the Gelfand-Naimark representation of functions that don't vanish at infinity?

Uncountable sum of vectors in a Hilbert Space