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WEIGHTEDCOMPOSITIONOPERATORSBETWEENVECTOR-VALUEDLIPSCHITZFUNCTIONSPACES B J M A BanachJ.Math.Anal.7(2013),no.1,59–72

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Banach J. Math. Anal. 7 (2013), no. 1, 59–72

B

anach

J

ournal of

M

athematical

A

nalysis ISSN: 1735-8787 (electronic)

www.emis.de/journals/BJMA/

WEIGHTED COMPOSITION OPERATORS BETWEEN VECTOR-VALUED LIPSCHITZ FUNCTION SPACES

K. ESMAEILI AND H. MAHYAR∗ Communicated by K. Jarosz

Abstract. We give necessary and sufficient conditions for the boundedness and compactness of weighted composition operators between spaces of vector- valued Lipschitz functions. We then show that a bounded separating linear operator between these spaces is indeed a weighted composition operator.

Department of Mathematics, Kharazmi University, 50, Taleghani Ave., 15618, Tehran, iran.

E-mail address: [email protected] E-mail address: [email protected]

Date: Received: 4 May 2012; Revised: 8 June 2012; Accepted: 15 June 2012.

∗ Corresponding author.

2010Mathematics Subject Classification. Primary 47B33; Secondary 46E40, 47B38.

Key words and phrases. Vector-valued Lipschitz function space, weighted composition oper- ator, compact linear operator, separating map, disjointness preserving operator.

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