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Let \(\displaystyle (T_{n}) \)be a sequence in \(\displaystyle {B(l_2}\) given by
\(\displaystyle T_{n}(x)=(2^{-1}x_{1},....,2^{-n}x_{n},0,0,....). \)Show that \(\displaystyle T_{n}->T\) given by
\(\displaystyle T(x)==(2^{-1}x_{1},2^{-2}x_{2},0,0,....). \)
I get a sequence of geometric series as my answer for the norm, but not sure whether that's correct.
\(\displaystyle T_{n}(x)=(2^{-1}x_{1},....,2^{-n}x_{n},0,0,....). \)Show that \(\displaystyle T_{n}->T\) given by
\(\displaystyle T(x)==(2^{-1}x_{1},2^{-2}x_{2},0,0,....). \)
I get a sequence of geometric series as my answer for the norm, but not sure whether that's correct.