How to show that the spectrum of $T_y$ is equal to the range of $y$
Given $y\in C[0,1]$ and $T_y: C[0,1] \rightarrow C[0,1]: x\mapsto x\cdot y$
Any help is appreciated, thanks.
2026-03-27 15:19:12.1774624752
How to show that the spectrum is equal to the range of $y$
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Here's a hint:
$$u\mapsto (\lambda - T_y)u = \lambda u - y u = (\lambda - y)u$$
is invertible for which $\lambda$?