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Linear operators of Banach spaces with range in Lipschitz algebras

Article 10, Volume 42, Issue 1, February 2016, Page 69-78  XML PDF (124 K)
Document Type: Research Paper
Authors
H. Mahyar ; A. Golbaharan
Department of Mathematics‎, ‎Faculty of Mathematical Sciences and‎ ‎Computer‎, ‎Kharazmi University‎, ‎50‎, ‎Taleghani Ave.‎, ‎15618‎, ‎Tehran‎, Iran.
Abstract
In this paper, a complete description concerning linear operators
of Banach spaces with range in Lipschitz algebras $lip_al(X)$ is
provided. Necessary and sufficient conditions are established to
ensure boundedness and (weak) compactness of these operators.
Finally, a lower bound for the essential norm of such operators is
obtained.
Keywords
Lipschitz algebra; compact linear operator; weakly compact linear operator; essential norm
Main Subjects
46-XX Functional Analysis; 47-XX Operator theory
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