Kunze Linear Algebra · Problem 6.4.9

Elementary Canonical Forms

Mathematics — Methods · indefinite-integral-invariant-subspaces

Problem

Let

T

be the indefinite integral operator

(Tf)(x) = \int_0^x f(t)\, dt

on the space of continuous functions on the interval

[0, 1]

. Is the space of polynomial functions invariant under

T

? The space of differentiable functions? The space of functions which vanish at

x = \frac{1}{2}