On sequence spaces defined by a sequence of moduli and an extension of Kuttner’s theorem

  • Virge Soomer University of Tartu


Let  A = (ank) be an infinite matrix with  limnkank ≠ 0, and let p=(pk) be a sequence of positive real numbers. If 1≤pk<H<∞, then the strong A-summability field (with the exponent p) is included in the summability field of A. But the result known as Kuttner’s theorem asserts that if 0<pk=˜p<1 and A is regular, then there is a sequence which is strongly (C,1)-summable but which is not A-summable. This result was extended by Thorpe (cf. Theorem 6) and Maddox (cf. [8] and [9]). The purpose of the present paper is to extend the results of Thorpe and Maddox to a lacunary strong summability with respect to a sequence of modulus functions.


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Author Biography

Virge Soomer, University of Tartu

Institute of Pure Mathematics