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A NOTE ON TRIANGULAR OPERATORS ON SMOOTH SEQUENCE SPACES
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Date
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
Collections
Graduate School of Natural and Applied Sciences, Article
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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.