Isometric isomorphism between $L^2$ and $mathcal{L}^2$
$begingroup$
I was reading and trying to understand the proof that the space $mathcal{L}^2 (mathcal{H})$ (Hilbert-Schmidt operators) is made by all the $T_K:L^2(X,mu) rightarrow L^2(X,mu)$ with $K in L^2(X times X, mu times mu)$.
Basically we assume $T in mathcal{L}^2$ and show $K in L^2(X times X, mu times mu) $ such that $T = T_K$. I really don't understand pretty much about the proof.. anyone could help?
functional-analysis hilbert-spaces compact-operators
asked Jan 10 at 16:06
James ArtenJames Arten
13411
$endgroup$
add a comment |
$begingroup$
I was reading and trying to understand the proof that the space $mathcal{L}^2 (mathcal{H})$ (Hilbert-Schmidt operators) is made by all the $T_K:L^2(X,mu) rightarrow L^2(X,mu)$ with $K in L^2(X times X, mu times mu)$.
Basically we assume $T in mathcal{L}^2$ and show $K in L^2(X times X, mu times mu) $ such that $T = T_K$. I really don't understand pretty much about the proof.. anyone could help?
functional-analysis hilbert-spaces compact-operators
asked Jan 10 at 16:06
James ArtenJames Arten
13411
$endgroup$
add a comment |
$begingroup$
I was reading and trying to understand the proof that the space $mathcal{L}^2 (mathcal{H})$ (Hilbert-Schmidt operators) is made by all the $T_K:L^2(X,mu) rightarrow L^2(X,mu)$ with $K in L^2(X times X, mu times mu)$.
Basically we assume $T in mathcal{L}^2$ and show $K in L^2(X times X, mu times mu) $ such that $T = T_K$. I really don't understand pretty much about the proof.. anyone could help?
functional-analysis hilbert-spaces compact-operators
asked Jan 10 at 16:06
James ArtenJames Arten
13411
$endgroup$
I was reading and trying to understand the proof that the space $mathcal{L}^2 (mathcal{H})$ (Hilbert-Schmidt operators) is made by all the $T_K:L^2(X,mu) rightarrow L^2(X,mu)$ with $K in L^2(X times X, mu times mu)$.
Basically we assume $T in mathcal{L}^2$ and show $K in L^2(X times X, mu times mu) $ such that $T = T_K$. I really don't understand pretty much about the proof.. anyone could help?
functional-analysis hilbert-spaces compact-operators
functional-analysis hilbert-spaces compact-operators
asked Jan 10 at 16:06
James ArtenJames Arten
13411
asked Jan 10 at 16:06
James ArtenJames Arten
13411
asked Jan 10 at 16:06
James ArtenJames Arten
13411
asked Jan 10 at 16:06
James ArtenJames Arten
13411
asked Jan 10 at 16:06
James ArtenJames Arten
13411
13411
add a comment |
add a comment |
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