A NOTE ON TRIANGULAR OPERATORS ON SMOOTH SEQUENCE SPACES

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2019-06-01
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.
Citation Formats
E. Uyanik and M. H. Yurdakul, “A NOTE ON TRIANGULAR OPERATORS ON SMOOTH SEQUENCE SPACES,” pp. 343–347, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30105.