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- W1969173863 abstract "In this paper a characterization of those quasinormal operators having the double commutant property is obtained. That is, a necessary and sufficient condition is given that a quasinormal operator $T$ satisfy the equation ${ T} '' = mathcal {A}(T)$, the weakly closed algebra generated by $T$ and $1$. In particular, it is shown that every pure quasinormal operator has the double commutant property. In addition two new representation theorems for certain quasinormal operators are established. The first of these represents a pure quasinormal operator $T$ as multiplication by $z$ on a subspace of an ${L^2}$ space whenever there is a vector $f$ such that ${ |T{|^k}{T^j}f: k, j geqslant 0}$ has dense linear span. The second representation theorem applies to those pure quasinormal operators $T$ such that ${T^{ast }}T$ is invertible. The second of these representation theorems will be used to determine which quasinormal operators have the double commutant property." @default.
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- W1969173863 date "1982-04-01" @default.
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- W1969173863 title "The Structure of Quasinormal Operators and the Double Commutant Property" @default.
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- W1969173863 doi "https://doi.org/10.2307/1999866" @default.
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