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Results tagged with banach-algebras
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user 86277
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Annihilator property dual
Let $G$ be a locally compact group and $\phi$ be in $ L^{\infty}(G)$ that annihilates $I$, where $I$ is a closed ideal of $ L^1(G)$, so by duality we have:
$$\int_G f(y)\phi(y)dy=0$$
for all $f\in I$ …
- 399
1
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Annihilator property dual
Really, I prove that if $f\in I$, then $\check{f}\in I$ where $I$ is a closed ideal of $L^1(G)$ and $\check{f}(x)=f(x^{-1})$ for every unimodular group $G$. Therefore since $\phi$ annihilate $I$. so
…
- 399
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Ideals of $L^1(G)$
For abelian case, close ideal of $L^1(G)$ is equal to translation invariant subspace of $L^1(G)$.[ please see: W.Rudin, Harmonic analysis on semigroup]
In general you can see [ Folland, Harmonic analy …
- 399