Chapter 4.2, Problem 36E

Find out which of the transformations in Exercises 1 through 50 are linear. For those that are linear, determine whether they are isomorphisms.

In Exercises 33 through 36, V denotes the space of infinite sequences of real numbers.

36. $T\left(f\left(t\right)\right)=\left(f\left(0\right),f\left(1\right),f\left(2\right),f\left(3\right),\mathrm{...}\right)$ from P to V, where P denotes the space of all polynomials