Advances in Functional Analysis and Approximation Theory
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".
Deadline for manuscript submissions: 20 November 2025 | Viewed by 71
Special Issue Editor
Special Issue Information
Dear Colleagues,
Banach space theory has been a big and central axis in functional analysis since its systematic investigation by Stefan Banach in 1930s. There are various fields in Banach space theory. One of the most important properties in Banach space theory is the approximation property, which was systematically studied by Grothendieck in 1950s. It not only deserves to be studied independently in itself, but also to be studied along with the theory of tensor norms and operator ideals for Banach spaces. Since that time, the approximation property has been intensively studied from various points of view by many mathematicians to solve the problems left behind. For instance, this area was recently concentrically studied to solve whether the metric approximation property and the approximation property are equivalent for dual spaces. Approximate identities in Banach algebra theory presented standard tools in harmonic analysis, and they have been independently developed since 1970s. Some relationships exist between approximation properties and approximate identities. For instance, the Banach algebra K(X) of compact operators on every Banach space X has a bounded left approximate identity if, and only if, X has the bounded compact approximation property. But its unbounded version is open, more precisely, it is not known whether X has the compact approximation property if K(X) has a left approximate identity.
The aim of this Special Issue of Mathematics is to collate recent research trends in approximation properties, approximate identities, and some areas of Banach space theory. Thus, research papers and review articles that consider problems in the areas of approximation properties and approximate identities, as well as developments of Banach space theory, are welcome.
Prof. Dr. Ju Myung Kim
Guest Editor
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Keywords
- approximation property
- approximate identity
- Banach space
- operator ideal
- tensor norm
- Banach algebra
- operator theory
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