A NOTE ON TRIANGULAR OPERATORS ON SMOOTH SEQUENCE SPACES


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Uyanik E., YURDAKUL M. H.

OPERATORS AND MATRICES, cilt.13, ss.343-347, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 13 Konu: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.7153/oam-2019-13-24
  • Dergi Adı: OPERATORS AND MATRICES
  • Sayfa Sayıları: ss.343-347

Özet

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.