Sociedad Colombiana de Matemáticas:Publicaciones
Revista Colombiana de Matemáticas
Volumen 36 [1] (2002)Páginas 29 - 48

Schauder bases in an abstract setting

István Kovács
University of Kentucky, Lexintong, USA
Arpád Száz
University of Debrecen, HUNGARY

Abstract. By using some generalized Riemann integrals instead of ordinary sums and multiplication systems of Banach spaces instead of Banach spaces, we establish some natural generalizations of the most basic facts on Schauder bases so that Hamel bases, and some other important unconditional bases, could also be included.

Palabras claves. Defining nets for integration, multiplication systems of Banach spaces, generalized Riemann integrals and Schauder bases.

Codigo AMS. 2000 Mathematics Subject Classification. Primary: 26A42. Secondary: 46B15.

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