Compact differences of composition operators on weighted Dirichlet spaces

• Autorzy: Robert Allen , Katherine Heller , Matthew Pons
• Języki publikacji: EN

Abstrakty

EN

Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S 2, the space of analytic functions whose first derivative is in H 2, and then use Calderón’s complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.

Słowa kluczowe

EN

Composition operator; Compact difference; Weighted Dirichlet space; Complex interpolation

Kategorie tematyczne

• 46E20: Hilbert spaces of continuous, differentiable or analytic functions
• 47B32: Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
• 47B33: Composition operators

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 7
• Strony: 1040-1051

Daty

wydano

2014-07-01

online

2014-04-03

Twórcy

autor

Robert Allen

• University of Wisconsin at La Crosse

autor

Katherine Heller

• North Central College

autor

Matthew Pons

• North Central College

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0397-3