JournalszaaVol. 12, No. 1pp. 179–182

λ\lambda-Convergence and λ\lambda-Conullity

  • W. Beekmann

    Fernuniversität-GHS, Hagen, Germany
  • S.-C. Chang

    Brock University, St. Catharines, Canada
$\lambda$-Convergence and $\lambda$-Conullity cover
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Abstract

The notions of λ\lambda-convergence and λ\lambda-summabihty was first defined a couple of decades ago by C. Kangro and has been further studied by Kangro and his school at Tartu University. In analogy to the usual notions of coregularity and conullity of conservative (matrix-) methods, he has introduced, inter alia, λ\lambda-coregularity and λ\lambda-conullity for λ\lambda-conservative matrices. Here we compare λ\lambda-conullity with the general notion of conullity of an FKFK-space with respect to a subspace which was introduced in [2]. To this end we show that the space cλc^{\lambda} of all λ\lambda-convergent sequences is of type cDc_D, a summability domain. As a consequence, we prove that the space of all sequences that are λ\lambda-summable by a given matrix AA is a summability domain cEc_E for some matrix EE.

Cite this article

W. Beekmann, S.-C. Chang, λ\lambda-Convergence and λ\lambda-Conullity. Z. Anal. Anwend. 12 (1993), no. 1, pp. 179–182

DOI 10.4171/ZAA/572