Uniqueness of Bases for almost linear spaces

Abstract

O. Mayer[9] introduced an almost linear space (als), a generalization of a linear space. The notion of a basis for an als was introduced by G. Godini[3]. Later, man properties of an als established by a number of authors. In this paper, we prove that the cardinality of bases for an als is unique. All spaces involved in this paper are over the real field $R$. Let us denote by $R_+$ the set ${\lambda \in R : \lambda \geq 0}$. We recall some definitions used in this paper.

Keywords

• Almost linear space;
• Almost linear subspace

File

Download PDF

References

1. Normed linear spaces M. M. Day
2. Pure and applied Mathematics v.7 Linear operators N. Dunford;J. Schwartz
3. Proceedings of the 12th Winter School on Abstract Analysis (Srni 1984). Suppl. Rend. Circ. Mat. Palermo Ⅱ. Ser. v.5 An approach to generalizing Banach spaces: Normed almost linear spaces G. Godini
4. J. Approx. Theory v.43 A framework for best simultaneous approximation: Normed almost linear spaces G. Godini
5. Math. Ann. v.279 On Normed Almost Linear Spaces G. Godini
6. Comm. Korean Math. Soc. v.10 Reflexivity of normed almost linear spaces S. H. Lee
7. J. Korea Soc. of Math. Edu. (Series B), The Pure and Applied Math. v.2 Basis for almost linear spaces G. Godini
8. Ph. D. Thesis Normed almost linear spaces G. Godini
9. Computing v.5 Algebraische und metrische strukturen in der intervallrechnung und einige anwendungen O. Mayer