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- Tue Nov 10, 2015 5:50 pm
- Forum: Functional Analysis
- Topic: Linear and bounded operator.
- Replies: 1
- Views: 2363
Re: Linear and bounded operator.
We define \(\displaystyle{T:\mathbb{l}_{2}(\mathbb{N})\longrightarrow \mathbb{l}_{2}(\mathbb{N})}\) by \(\displaystyle{a=\left(a_{n}\right)_{n\in\mathbb{N}}\mapsto T(a):=\left(0,a_1,a_2,...,a_n,a_{n+1},...\right)}\) . Prove that the function \(\displaystyle{T}\) is linear, bounded and \(\displaysty...