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- W2022689148 abstract "For every, possibly unbounded, multiplication operator in $L^p$-space, $pin ]0,infty[$, on finite separable measure space we show that multicyclicity, multi-*-cyclicity, and multiplicity coincide. This result includes and generalizes Bram's much cited theorem from 1955 on bounded *-cyclic normal operators. It also includes as a core result cyclicity of the multiplication operator $M_z$ by the complex variable $z$ in $L^p(mu)$ for every Borel measure $mu$ on $C$. The concise proof is based in part on the result that the function $e^{-|z|^2}$ is a *-cyclic vector for $M_z$ in $C_0(C)$ and further in $L^p(mu)$. We characterize topologically those locally compact sets $Xsubset C$, for which $M_z$ in $C_0(X)$ is cyclic." @default.
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- W2022689148 date "2013-07-09" @default.
- W2022689148 modified "2023-09-27" @default.
- W2022689148 title "Cyclicity for Unbounded Multiplication Operators in Lp- and C0-Spaces" @default.
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