THE SPECTRUM OF q-CESARO MATRICES ON c AND ITS VARIOUS SPECTRAL DECOMPOSITION FOR 0 < q < 1


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DURNA N. , TÜRKAY M. E.

OPERATORS AND MATRICES, vol.15, no.3, pp.795-813, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.7153/oam-2021-15-55
  • Title of Journal : OPERATORS AND MATRICES
  • Page Numbers: pp.795-813
  • Keywords: q-Hausdorff matrices, Lower bound problem, q-Cesaro matrices, spectrum, fine spectrum, GENERALIZED DIFFERENCE OPERATOR, SEQUENCE-SPACES L(P), DOUBLE-BAND MATRICES, FINE SPECTRUM, FACTORABLE MATRICES, SUBDIVISIONS, 2ND-ORDER, B(R, S)

Abstract

One of q-analogs of the Cesaro matrix of order one is the triangular matrix with nonzero entries c(nk) = q(n-k)/1+q+...+q(n), 0 <= k <= n, where q is an element of [0,1]. In this article, we will determine the spectrum of this matrix on the space of convergent sequences c. We will also obtain the fine spectral decomposition in the sense of Goldberg and a non-discrete spectral decomposition of the obtained spectrum.