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.

Full Text

     

M. S. Ramanujan ¹

Affiliations
1 Ramanujan Institute of Mathematics, Madras, IN

Abstract

The problem of the total translativity of Holder and Cesaro methods has been considered earlier by Kuttner [3]. In the present note we are concerned with the more general problem of the total translativity of Hausdorff methods and we prove that a Hausdorff method, satisfying suitable restrictions, is totally translative if, and only if, it is the Cesaro method or a trivial modification of that method.

Full Text

     

M. S. Ramanujan ¹

Affiliations
1 Aunainalai University, IN

Abstract

Let U = ^∞∑_{I =0} u_i be a series, convergent or not, and let (a_nk) be an infinite square matrix. If for n = 0,1, 2 , . . . The series ∑a_nk u_k converges to some value v_n, and if also the series ∑ v_n converges, then U is said to be summable by the series-to-series transformation A = (a_nk) to the sum ∑ v_n.

Full Text