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Results tagged with banach-algebras
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user 61771
1
vote
Rigorous justification for this formal solution to $f(x+1)+f(x)=g(x)$
Just to add another answer to the pile...
I suspect that the 'magic' observed here may be related to so-called local spectral theory. It is possible to do quite a lot (at least in the Banach space se …
- 778
1
vote
Accepted
Function in $B(\mathbb{R})$
You may be aware of this already, but a similar (if not the same) question is addressed in Rudin's Fourier Analysis on Groups. Material on the same subject can be found in Katznelson's Harmonic analys …
- 778
4
votes
0
answers
84
views
Can a spectral projection fail to preserve a closed invariant subspace of its parent operator?
Let $X$ be a complex Banach space, and let $T:X\longrightarrow X$ be a bounded linear operator. Let $\sigma_1$ and $\sigma_2$ be disjoint compact subsets of $\mathbb{C}$ for which $\sigma_1\cup \sigma …
- 778