Abstract
AbstractThe necessary and sufficient conditions for both the Kadec–Klee property as well as the Kadec–Klee property with respect to the coordinatewise convergence in Orlicz–Lorentz sequence spaces equipped with the Orlicz norm and generated by arbitrary Orlicz functions as well as any non-increasing weight sequences are given. Moreover, for their subspaces of elements with an order continuous norm the full characterization of the Kadec–Klee property with respect to the coordinatewise convergence is presented. Some tools useful in the proofs of the main results are also provided.
Funder
NSF of China
National Science Centre, Poland
Publisher
Springer Science and Business Media LLC
Subject
General Mathematics,Theoretical Computer Science,Analysis
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