Invariant dissipative operators on locally compact groups (Q1086488)
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scientific article; zbMATH DE number 3983935
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Invariant dissipative operators on locally compact groups |
scientific article; zbMATH DE number 3983935 |
Statements
Invariant dissipative operators on locally compact groups (English)
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1987
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Let G be a Lie group and \(C_ 0(G)\) the Banach space of all continuous functions on G vanishing at infinity. In this note we show that if the Lie algebra of G is not compact, then the closure \=D of a left invariant elliptic differential operator D on G has a restriction T such that T is also a left invariant closed dissipative linear operator in \(C_ 0(G)\) satisfying the inequality \(Range(I-T)\subsetneqq c_ 0(G)\).
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Lie group
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Lie algebra
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left invariant elliptic differential operator
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closed dissipative linear operator
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