Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions

José Bonet; Paweł Domański; Mikael Lindström

doi:10.4153/CMB-1999-016-x

Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions

José Bonet
, Paweł Domański
, Mikael Lindström

Matematik

Forskningsoutput: Tidskriftsbidrag › Artikel › Vetenskaplig › Peer review

104 Citeringar (Scopus)

Sammanfattning

Every weakly compact composition operator between weighted Banach spaces H^∞_v of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space H^∞_v are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

Originalspråk	Engelska
Sidor (från-till)	139-148
Antal sidor	10
Tidskrift	Canadian Mathematical Bulletin
Volym	42
Nummer	2
DOI	https://doi.org/10.4153/CMB-1999-016-x
Status	Publicerad - juni 1999
MoE-publikationstyp	A1 Tidskriftsartikel-refererad

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title = "Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions",

abstract = "Every weakly compact composition operator between weighted Banach spaces H∞v of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space H∞v are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.",

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author = "Jos{\'e} Bonet and Pawe{\l} Doma{\'n}ski and Mikael Lindstr{\"o}m",

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AU - Bonet, José

AU - Domański, Paweł

AU - Lindström, Mikael

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Y1 - 1999/6

N2 - Every weakly compact composition operator between weighted Banach spaces H∞v of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space H∞v are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

AB - Every weakly compact composition operator between weighted Banach spaces H∞v of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space H∞v are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

KW - Compact operator

KW - Composition operator

KW - Weakly compact operator

KW - Weighted Banach spaces of holomorphic functions

UR - https://www.scopus.com/pages/publications/0000410554

U2 - 10.4153/CMB-1999-016-x

DO - 10.4153/CMB-1999-016-x

M3 - Article

AN - SCOPUS:0000410554

SN - 0008-4395

VL - 42

SP - 139

EP - 148

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

IS - 2

ER -

Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions

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