Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 265-285

IDEAL TOPOLOGIES AND CORRESPONDING APPROXIMATION PROPERTIES

Sonia Berrios and Geraldo Botelho

Universidade Federal de Uberlândia, Faculdade de Matemática
38.400-902 - Uberlândia, Brazil; soniles 'at' famat.ufu.br

Universidade Federal de Uberlândia, Faculdade de Matemática
38.400-902 - Uberlândia, Brazil; botelho@ufu.br

Abstract. We propose a unifying approach to numerous approximation properties in Banach spaces studied from the 1930s up to our days. To do so, we introduce the concept of ideal topology and say that a Banach space E has the (I,J,τ)-approximation property if E-valued operators belonging to the operator ideal I can be approximated, with respect to the ideal topology τ, by operators belonging to the operator ideal J. This concept recovers many classical/recent approximation properties as particular instances and several important known results are particular cases of more general results that are valid in this general framework.

2010 Mathematics Subject Classification: Primary 46B28, 46A32, 47L20, 47B10, 46G25, 47L22.

Key words: Approximation property, operator ideal, Banach space, projective tensor product.

Reference to this article: S. Berrios and G. Botelho: Ideal topologies and corresponding approximation properties. Ann. Acad. Sci. Fenn. Math. 41 (2016), 265-285.

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doi:10.5186/aasfm.2016.4117