Weak and Strong Density of Compositions

The convergence in various topologies of sequences of inner superposition (composition) operators acting between Lebesgue spaces and of their linear combinations is studied. In particular, the sequential density results for the linear span of such operators is proved for the weak, weak continuous an...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2000-08, Vol.352 (8), p.3707-3721
Main Authors: De Pascale, Luigi, Stepanov, Eugene
Format: Article
Language:English
Subjects:
Density
Differential equations
Eigenfunctions
Generating function
Homeomorphism
Lebesgue spaces
Linear transformations
Mathematical functions
Topological spaces
Topological theorems
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Summary:The convergence in various topologies of sequences of inner superposition (composition) operators acting between Lebesgue spaces and of their linear combinations is studied. In particular, the sequential density results for the linear span of such operators is proved for the weak, weak continuous and strong operator topologies.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-00-02510-1