Approximation of \(p\)-multiplier operators via their spectral projections. (English) Zbl 1132.42305
Summary: Conditions for a \(p\)-multiplier \(\psi: {\mathbb{Z}} \to {\mathbb{C}}\) are presented which ensure that the corresponding operator \(T_{\psi}\), acting in \(L^p({\mathbb{T}})\), can be approximated by linear combinations of \(p\)-multiplier projections coming from the uniform operator closed, unital algebra of operators generated by \(T_{\psi}\). Functions of bounded variation on \({\mathbb{Z}}\) play an important role, as do certain \(\Lambda (p)\)-sets.
MSC:
| 42A45 | Multipliers in one variable harmonic analysis |
| 47A58 | Linear operator approximation theory |
| 47B40 | Spectral operators, decomposable operators, well-bounded operators, etc. |
| 41A45 | Approximation by arbitrary linear expressions |
| 47A25 | Spectral sets of linear operators |
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