Answer to Question #6265 in Complex Analysis for Halime

Question

Let S; T : L^2(0,infinite) -> L^(o,infiniti) be given by
(Sf)(t) = f(2t), (Tf)(t)=f(t/2), f is an element of L^2 (0,infinite).
You are given that S and T are linear mappings L^2(0,infinite) ->L^2(0,infinite), and you need not prove this fact.
i) Calculatr ||S||
ii) Show that T*=2S. Determine S*

[Hint: The usual rules for integration by substitutions also work for the Lebesque integral You need not justify this fact. }