Approximation of operators in dual spaces by adjoint operators

Let X and Y be Banach spaces, and let T : Y * → X * be a linear continuous operator. We discuss the possibility of approximation of T by adjoint operators S * : Y * → X * in the topology of compact convergence in L( Y * , X * ) and in the topology of pointwise X × Y * −convergence in L( Y * , X * )...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2011-03, Vol.173 (5), p.632-642
Main Author: Reinov, O. I.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:Let X and Y be Banach spaces, and let T : Y * → X * be a linear continuous operator. We discuss the possibility of approximation of T by adjoint operators S * : Y * → X * in the topology of compact convergence in L( Y * , X * ) and in the topology of pointwise X × Y * −convergence in L( Y * , X * ) and also approximation of the operator T * ∣ X : X → Y ** by operators from X to Y in the corresponding topologies. Bibliography: 11 titles.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-011-0263-4