# Compact differences of composition operators on weighted Dirichlet spaces

Robert Allen; Katherine Heller; Matthew Pons

Open Mathematics (2014)

- Volume: 12, Issue: 7, page 1040-1051
- ISSN: 2391-5455

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topRobert Allen, Katherine Heller, and Matthew Pons. "Compact differences of composition operators on weighted Dirichlet spaces." Open Mathematics 12.7 (2014): 1040-1051. <http://eudml.org/doc/269467>.

@article{RobertAllen2014,

abstract = {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.},

author = {Robert Allen, Katherine Heller, Matthew Pons},

journal = {Open Mathematics},

keywords = {Composition operator; Compact difference; Weighted Dirichlet space; Complex interpolation; composition operator; compact difference; weighted Dirichlet space; complex interpolation},

language = {eng},

number = {7},

pages = {1040-1051},

title = {Compact differences of composition operators on weighted Dirichlet spaces},

url = {http://eudml.org/doc/269467},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Robert Allen

AU - Katherine Heller

AU - Matthew Pons

TI - Compact differences of composition operators on weighted Dirichlet spaces

JO - Open Mathematics

PY - 2014

VL - 12

IS - 7

SP - 1040

EP - 1051

AB - 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.

LA - eng

KW - Composition operator; Compact difference; Weighted Dirichlet space; Complex interpolation; composition operator; compact difference; weighted Dirichlet space; complex interpolation

UR - http://eudml.org/doc/269467

ER -

## References

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