# Weakly compact composition operators on spaces of Lipschitz functions

Weakly compact composition operators on spaces of Lipschitz functions Let $$X$$ X be a pointed compact metric space such that $${\mathrm {lip}}_0(X)$$ lip 0 ( X ) has the uniform separation property. We prove that every weakly compact composition operator on spaces of Lipschitz functions $${\mathrm {lip}}_0(X)$$ lip 0 ( X ) and $${\mathrm {Lip}}_0(X)$$ Lip 0 ( X ) is compact. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Weakly compact composition operators on spaces of Lipschitz functions

, Volume 19 (4) – Mar 8, 2015
9 pages

/lp/springer_journal/weakly-compact-composition-operators-on-spaces-of-lipschitz-functions-rAjSb4300G
Publisher
Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-015-0329-5
Publisher site
See Article on Publisher Site

### Abstract

Let $$X$$ X be a pointed compact metric space such that $${\mathrm {lip}}_0(X)$$ lip 0 ( X ) has the uniform separation property. We prove that every weakly compact composition operator on spaces of Lipschitz functions $${\mathrm {lip}}_0(X)$$ lip 0 ( X ) and $${\mathrm {Lip}}_0(X)$$ Lip 0 ( X ) is compact.

### Journal

PositivitySpringer Journals

Published: Mar 8, 2015

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