# FA24

Let $L^2[a,b]=\left\{f:\int_a^b\left|f(t)\right|^2 dt < \infty\right\}\,$ and define $||f||=\left(\int_a^b\left|f(t)\right|^2 dt\right)^{1/2}\,$. Show that
$(Tf)(t) = \int_a^b K(s,t)f(s)ds\,$
defines a bounded linear operator on $L^2[a,b]\,$ when $K(s,t)\,$ is a continuous function on $[a,b]\times[a,b]\,$. Estimate the norm of $T\,$.