A NOTE ON TRIANGULAR OPERATORS ON SMOOTH SEQUENCE SPACES

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UYANIK E., YURDAKUL M. H.

OPERATORS AND MATRICES, vol.13, no.2, pp.343-347, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.7153/oam-2019-13-24
  • Journal Name: OPERATORS AND MATRICES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.343-347
  • Yozgat Bozok University Affiliated: Yes

Abstract

For a scalar sequence (theta(n))(n is an element of N), let C be the matrix defined by c(n)(k) = theta(n-k+1) if n >= k, c(n)(k) = 0 if n < k. The map between Kothe spaces lambda(A) and lambda(B) is called a Cauchy Product map if it is determined by the triangular matrix C. In this note we introduced some necessary and sufficient conditions for a Cauchy Product map on a nuclear Kothe space lambda(A) to nuclear G(1) - space lambda(B) to be linear and continuous. Its transpose is also considered.