Izvorni znanstveni članak

https://doi.org/10.3336/gm.49.2.13

The metric approximation property in non-archimedean normed spaces

Cristina Perez-Garcia ; Department of Mathematics, Facultad de Ciencias, Universidad de Cantabria , Avda. de los Castros s/n, 39071, Santander , Spain
Wilhelmus H. Schikhof ; Weezenhof 3607, 6536 HC Nijmegen, The Netherlands

Sažetak

A normed space E over a rank 1 non-archimedean valued field K has the metric approximation property (MAP) if the identity on E can be approximated pointwise by finite rank operators of norm 1. Characterizations and hereditary properties of the MAP are obtained. For Banach spaces E of countable type the following main result is derived: E has the MAP if and only if E is the orthogonal direct sum of finite-dimensional spaces (Theorem 4.9). Examples of the MAP are also given. Among them, Example 3.3 provides a solution to the following problem, posed by the first author in [8, 4.5]. Does every Banach space of countable type over K have the MAP?

Ključne riječi

Non-archimedean normed spaces; pseudoreflexivity; metric approximation property; finite-dimensional decomposition

Hrčak ID:

130893

URI

https://hrcak.srce.hr/130893

Datum izdavanja:

18.12.2014.

Posjeta: 881 *