Λ(α)-Bases and Nuclear Spaces

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Authors

  • E. D. Dubinsky
     Mathematics Department, Clarkson College of Technology, Potsdam, N. Y. 13676 ,US
  • M. S. Ramanujan
     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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Published

1972-12-01

How to Cite

Dubinsky, E. D., & Ramanujan, M. S. (1972). Λ(α)-Bases and Nuclear Spaces. The Journal of the Indian Mathematical Society, 36(3-4), 333–345. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/16676

Issue

Volume 36, Issue 3-4, September-December 1972

Section

Articles

License

Copyright (c) 1972 E. D. Dubinsky, M. S. Ramanujan

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

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A. S. DYNIN and B. S. MITIAGIN : Criterion for nuclearity in terms of approximative dimension, Bull. Acad. Polon. Sci. 8 (1960), 535-540.

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