The Journal of the Indian Mathematical Society

E. D. Dubinsky ¹, M. S. Ramanujan ²

Affiliations
1 Mathematics Department, Clarkson College of Technology, Potsdam, N. Y. 13676, US
2 Department of Mathematics, University of Michigan, Ann Arbor, MI 48104, US

Abstract

IN A STUDY of the properties of bases in nuclear Frechet spaces, Dynin and Mitiagin [5] proved that in such spaces every Schauder basis is an absolute basis; another proof of this interesting result was given by Mitiagin [7]. Replacing the sequence space l₁ in the definition of nuclear maps by the nuclear sequence space Λ(α) of power series the second author initiated, in [10], a study of Λ(α)- nuclear spaces and this study is presented in greater depth in a recent paper of the authors [3]. In this paper we introduce the notion of Λ(α)-basis in locally convex spaces.

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