let $ 1 < P < + \infty $ and
$ T : L^{P} [ 0 , 1] \longrightarrow L^{P} [ 0 , 1]$ $ T ( f ( t)) = \int_{0}^{1} ( s^{2} + t^{2} ) f(s)ds$
How can we show that $ T $ is rank 2?
How is the Spectrum calculation?