Show that $\psi:L(E,L(E,F))\rightarrow L^2(E,F)$ given by $[\psi(T)](u,v)=[T(u)](v)$ is a linear homeomorphism
Let $E,F$ be Banach spaces. Denote by $L^2(E,F)$ the space of continuous bilinear applications $T:E^2\rightarrow F$ with norm $T=\underset {x_i_E≤1}{sup}{T(x_1,x_2)_F}$.
Show that $\psi:L(E,L(E,F))\rightarrow L^2(E,F)$ given by $[\psi(T)](u,v)=[T(u)](v)$ is a linear homeomorphism, first showing that $L^2(E,F)$ is Banach and then using the open mapping theorem.
Kp Yao
18
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.
 accepted
 99 views
 $30.00
Related Questions
 Find $\int\frac{dx}{2x^22x+1}$
 Evaluate $\int \frac{dx}{x \sqrt{1+\ln x}}$
 Calc 3 Question
 Not sure what I'm doing wrong
 Differentiate $\int_{\sin x}^{\ln x} e^{\tan t}dt$
 Compute $\lim_{x \rightarrow 0} \frac{1\arctan (\sin(x)+1)}{e^{x}1}$

Find a general solution for the lengths of the sides of the rectangular parallelepiped with the
largest volume that can be inscribed in the following ellipsoid  Find the domain of the function $f(x)=\frac{\ln (1\sqrt{x})}{x^21}$