Topological properties and matrix transformations of certain ordered generalized sequence spaces
In this note, we carry out investigations related to the mixed impact of ordering and topological structure of a locally convex solid Riesz space (X,τ) and a scalar valued sequence space λ, on the vector valued sequence space λ(X) which is formed and topologized with the help of λ and X, and vice ve...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171295000433 |
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| Summary: | In this note, we carry out investigations related to the mixed
impact of ordering and topological structure of a locally convex solid
Riesz space (X,τ) and a scalar valued sequence space λ, on the vector
valued sequence space λ(X) which is formed and topologized with the help
of λ and X, and vice versa. Besides,we also characterize o-matrix transformations
from c(X), ℓ∞(X) to themselves, cs(X) to c(X) and derive necessary
conditions for a matrix of linear operators to transform ℓ1(X) into a
simple ordered vector valued sequence space Λ(X). |
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| ISSN: | 0161-1712 1687-0425 |