The Question is as follows:(adsbygoogle = window.adsbygoogle || []).push({});

let A be a bounded domain in R^n and

Xm a series of real functions in L^2 (A).

if Xm converge weakly to X in L^2(A)

and (Xm)^2 converge weakly to Y in L^2(A)

then Y=X^2.

i don't know if the above theorem is true and could sure use any help i can get.

if anyone has any proof please post it... thanks.

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# Question about weak convergence in Hilbert space

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