Operators
Posted: Sun Mar 13, 2016 2:17 pm
Let \(\displaystyle{\left(X,||\cdot||\right)}\) be a normed space and \(\displaystyle{T\,,S\in\mathbb{B}(X)}\)
such that \(\displaystyle{T^2=T\,,S^2=S\,,T\circ S=S\circ T}\) .
Prove that either \(\displaystyle{T=S}\) or \(\displaystyle{||T-S||\geq 1}\) .
such that \(\displaystyle{T^2=T\,,S^2=S\,,T\circ S=S\circ T}\) .
Prove that either \(\displaystyle{T=S}\) or \(\displaystyle{||T-S||\geq 1}\) .