Linear Algebra Hoffman Kunze Chapter 3 example 5!
Let $R$ be the field of real numbers and let $V$ be the space of all
functions from $R$ into $R$ which are continuous. Define T by
$(Tf)(x)=\int^{x}_{0}f(t)dt$.
Then $T$ is a linear transformation from $V$ into $V$.
The last statement is not true, let $g$ be the zero function ($g(x)=0$,
for any $x$). $(Tg)(x)$ is equal to a class of functions in $V$ of the
form $B_{c}(x)=c$. So, there is no unique assignment for a certain
function from $V$.
Am I wrong somewhere?
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