Isometric Composition Operators on Lipschitz Spaces
Given pointed metric spaces X and Y , we characterize the basepoint-preserving Lipschitz maps ϕ from Y to X inducing an isometric composition operator C ϕ between the Lipschitz spaces Lip 0 ( X ) and Lip 0 ( Y ) , whenever X enjoys the peak property. This gives an answer to a question posed by Weave...
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| Veröffentlicht in: | Mediterranean journal of mathematics 2020-04, Vol.17 (2), Article 52 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Given pointed metric spaces
X
and
Y
, we characterize the basepoint-preserving Lipschitz maps
ϕ
from
Y
to
X
inducing an isometric composition operator
C
ϕ
between the Lipschitz spaces
Lip
0
(
X
)
and
Lip
0
(
Y
)
, whenever
X
enjoys the peak property. This gives an answer to a question posed by Weaver in his book [Lipschitz algebras. Second edition. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2018]. |
|---|---|
| ISSN: | 1660-5446 1660-5454 |
| DOI: | 10.1007/s00009-020-1488-6 |