The Journal of the Indian Mathematical Society

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Λ(α)-Bases and Nuclear Spaces


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

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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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  • Λ(α)-Bases and Nuclear Spaces

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Authors

E. D. Dubinsky
Mathematics Department, Clarkson College of Technology, Potsdam, N. Y. 13676, United States
M. S. Ramanujan
Department of Mathematics, University of Michigan, Ann Arbor, MI 48104, United States

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.