Topological structure of the set of weighted composition operators on weighted Bergman spaces of infinite order

José Bonet; Mikael Lindström; Elke Wolf

doi:10.1007/s00020-009-1706-x

Topological structure of the set of weighted composition operators on weighted Bergman spaces of infinite order

José Bonet^*
, Mikael Lindström
, Elke Wolf

^*Korresponderande författare för detta arbete

Matematik

Forskningsoutput: Tidskriftsbidrag › Artikel › Vetenskaplig › Peer review

7 Citeringar (Scopus)

Sammanfattning

We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H^∞) and L(H^∞_ν) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated.

Originalspråk	Engelska
Sidor (från-till)	195-210
Antal sidor	16
Tidskrift	Integral Equations and Operator Theory
Volym	65
Nummer	2
DOI	https://doi.org/10.1007/s00020-009-1706-x
Status	Publicerad - okt. 2009
MoE-publikationstyp	A1 Tidskriftsartikel-refererad

Finansiering

The research of José Bonet was partially supported by FEDER and MEC Project MTM 2007-62643 and Generalitat Valenciana project Prometeo/2008/101. Part of the present work was done during a stay of J. Bonet at the University of Paderborn in August 2008. The support of the Alexander von Humboldt Foundation is greatly appreciated.

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title = "Topological structure of the set of weighted composition operators on weighted Bergman spaces of infinite order",

abstract = "We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H∞) and L(H∞ν) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated.",

keywords = "Topological structure, Weighted Bergman space of infinite order, Weighted composition operator",

author = "Jos{\'e} Bonet and Mikael Lindstr{\"o}m and Elke Wolf",

note = "Funding Information: The research of Jos{\'e} Bonet was partially supported by FEDER and MEC Project MTM 2007-62643 and Generalitat Valenciana project Prometeo/2008/101. Part of the present work was done during a stay of J. Bonet at the University of Paderborn in August 2008. The support of the Alexander von Humboldt Foundation is greatly appreciated.",

year = "2009",

month = oct,

doi = "10.1007/s00020-009-1706-x",

language = "English",

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T1 - Topological structure of the set of weighted composition operators on weighted Bergman spaces of infinite order

AU - Bonet, José

AU - Lindström, Mikael

AU - Wolf, Elke

N1 - Funding Information: The research of José Bonet was partially supported by FEDER and MEC Project MTM 2007-62643 and Generalitat Valenciana project Prometeo/2008/101. Part of the present work was done during a stay of J. Bonet at the University of Paderborn in August 2008. The support of the Alexander von Humboldt Foundation is greatly appreciated.

PY - 2009/10

Y1 - 2009/10

N2 - We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H∞) and L(H∞ν) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated.

AB - We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H∞) and L(H∞ν) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated.

KW - Topological structure

KW - Weighted Bergman space of infinite order

KW - Weighted composition operator

UR - https://www.scopus.com/pages/publications/71549127718

U2 - 10.1007/s00020-009-1706-x

DO - 10.1007/s00020-009-1706-x

M3 - Article

AN - SCOPUS:71549127718

SN - 0378-620X

VL - 65

SP - 195

EP - 210

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 2

ER -

Topological structure of the set of weighted composition operators on weighted Bergman spaces of infinite order

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