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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

0 votes

Linear operator on polynomials and invariant sets of roots

For $l$ a linear form on this space take $T = j\circ l$ where $j$ is the inclusion of $\mathbb C$ into constant polynomials. This is not invertible.
InfiniteLooper's user avatar
1 vote

Relationship between $2 \to 2$ norm and $\infty \to 2$ norm

It is more a question on norms on spaces and not on operators as $\| \cdot \|_{N_1, N_3} \leq C \| \cdot \|_{N_2,N_3}$ if and only if $N_2 \leq \frac{1}{C} N_1$. Doing so if $l_{x,y}(z) = \left< x, z …
InfiniteLooper's user avatar