A NOTE ON TRIANGULAR OPERATORS ON SMOOTH SEQUENCE SPACES

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2019-06-01

Author

Uyanik, Elif
Yurdakul, Murat Hayrettin

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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.

Subject Keywords

Kothe spaces, Smooth sequence spaces, Cauchy product

URI

https://hdl.handle.net/11511/30105

Journal

OPERATORS AND MATRICES

DOI

https://doi.org/10.7153/oam-2019-13-24

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Graduate School of Natural and Applied Sciences, Article

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Citation Formats

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