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تسجيل مستخدم جديدWolffs Problem of Ideals in the Multipler Algebra on Weighted Dirichlet Space
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We establish an analogue of Wolffs theorem on ideals in $H^{infty}(mathbb{D})$ for the multiplier algebra of weighted Dirichlet space.
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We establish an analogue of Wolffs theorem on ideals in $H^{infty}(mathbb{D})$ for the multiplier algebra of Dirichlet space.
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er $n$ of $phi$ is $2$ or $3$, we show that $M_phi$ is reducible on $D$ if and only if $phi$ is equivalent to $z^n$. When the order of $phi$ is $4$, we determine the reducing subspaces for $M_phi$, and we see that in this case $M_phi$ can be reducible on $D$ when $phi$ is not equivalent to $z^4$. The same phenomenon happens when the order $n$ of $phi$ is not a prime number. Furthermore, we show that $M_phi$ is unitarily equivalent to $M_{z^n} (n > 1)$ on $D$ if and only if $phi = az^n$ for some unimodular constant $a$.
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