Isometric composition operators on weighted Dirichlet space

Han, Shi-An; Zhou, Ze-Hua

doi:10.1007/s10587-016-0235-4

Geodesic

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Isometric composition operators on weighted Dirichlet space

Han, Shi-An ; Zhou, Ze-Hua

Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 27-34.

Voir la notice de l'article dans Czech Digital Mathematics Library

Résumé

We investigate isometric composition operators on the weighted Dirichlet space

D_{α}

with standard weights

(1 - | z |^{2})^{α}

α > - 1

. The main technique used comes from Martín and Vukotić who completely characterized the isometric composition operators on the classical Dirichlet space

D

. We solve some of these but not in general. We also investigate the situation when

D_{α}

is equipped with another equivalent norm.

MR Zbl

DOI : 10.1007/s10587-016-0235-4

Classification : 46B04, 47B33, 47B38
Mots-clés : composition operator; weighted Dirichlet space; isometry

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Han, Shi-An; Zhou, Ze-Hua. Isometric composition operators on weighted Dirichlet space. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 27-34. doi : 10.1007/s10587-016-0235-4. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0235-4/

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