What is "local theory of Banach spaces"?
Volume 135 / 1999
Studia Mathematica 135 (1999), 273-298 DOI: 10.4064/sm-135-3-273-298
Banach space theory splits into several subtheories. On the one hand, there are an isometric and an isomorphic part; on the other hand, we speak of global and local aspects. While the concepts of isometry and isomorphy are clear, everybody seems to have its own interpretation of what "local theory" means. In this essay we analyze this situation and propose rigorous definitions, which are based on new concepts of local representability of operators.