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- W4298478611 abstract "Let $E$ and $F$ be Hilbert $C^*$-modules over a $C^*$-algebra $CAlg{A}$. New classes of (possibly unbounded) operators $t:Eto F$ are introduced and investigated. Instead of the density of the domain $Def(t)$ we only assume that $t$ is essentially defined, that is, $Def(t)^bot={0}$. Then $t$ has a well-defined adjoint. We call an essentially defined operator $t$ graph regular if its graph $Graph(t)$ is orthogonally complemented in $Eoplus F$ and orthogonally closed if $Graph(t)^{botbot}=Graph(t)$. A theory of these operators is developed. Various characterizations of graph regular operators are given. A number of examples of graph regular operators are presented ($E=C_0(X)$, a fraction algebra related to the Weyl algebra, Toeplitz algebra, Heisenberg group). A new characterization of affiliated operators with a $C^*$-algebra in terms of resolvents is given." @default.
- W4298478611 created "2022-10-02" @default.
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- W4298478611 date "2014-09-30" @default.
- W4298478611 modified "2023-09-23" @default.
- W4298478611 title "Unbounded Operators on Hilbert $C^*$-Modules" @default.
- W4298478611 doi "https://doi.org/10.48550/arxiv.1409.8523" @default.
- W4298478611 hasPublicationYear "2014" @default.
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