The optimal range of the Calderòn operator and its applications. (English) Zbl 1437.46036
Summary: We identify the optimal range of the Calderòn operator and that of the classical Hilbert transform in the class of symmetric quasi-Banach spaces. Further consequences of our approach concern the optimal range of the triangular truncation operator, operator Lipschitz functions, and commutator estimates in ideals of compact operators.
MSC:
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 47B10 | Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) |
| 46L51 | Noncommutative measure and integration |
| 46L52 | Noncommutative function spaces |
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 47L20 | Operator ideals |
| 47C15 | Linear operators in \(C^*\)- or von Neumann algebras |
Keywords:
symmetric function spaces; symmetric operator spaces; (quasi-)Banach space; Hilbert transform; triangular truncation operator; optimal symmetric range; semifinite von Neumann algebraReferences:
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