16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 6.2.13

Elementary Canonical Forms

Mathematics — Linear Algebra · integral-operator-no-characteristic-values

Problem

Let

V

be the vector space of all functions from

R

into

R

which are continuous, i.e., the space of continuous real-valued functions on the real line. Let

T

be the linear operator on

V

defined by

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

Prove that

T

has no characteristic values.