The dual spaces of sets of difference sequences of order m and matrix transformations
Let p = (pk}∞k=0be a bounded sequence of positive reals, m ∈ and u be s sequence of nonzero terms. If x = (xk}∞k=0is any sequence of complex numbers we write Δ(m)x for the sequence of the m-th order differences of x and Δ(m)uX = {x = (x}∞k=0:uΔ(m)x ∈ X} for any set X of sequences. We determine the α...
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th-cmuir.6653943832-612182018-09-10T04:06:55Z The dual spaces of sets of difference sequences of order m and matrix transformations Eberhard Malkowsky Mursaleen Suthep Suantai Mathematics Let p = (pk}∞k=0be a bounded sequence of positive reals, m ∈ and u be s sequence of nonzero terms. If x = (xk}∞k=0is any sequence of complex numbers we write Δ(m)x for the sequence of the m-th order differences of x and Δ(m)uX = {x = (x}∞k=0:uΔ(m)x ∈ X} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δ(m)uX for X = c0(p), c(p), l∞(p) and characterize some matrix transformations between these spaces Δ(m)X. © Springer-Verlag Berlin Heidelberg 2007. 2018-09-10T04:06:55Z 2018-09-10T04:06:55Z 2007-03-01 Journal 14398516 2-s2.0-34047218579 10.1007/s10114-005-0719-x https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=34047218579&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/61218 |
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Mathematics |
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Mathematics Eberhard Malkowsky Mursaleen Suthep Suantai The dual spaces of sets of difference sequences of order m and matrix transformations |
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Let p = (pk}∞k=0be a bounded sequence of positive reals, m ∈ and u be s sequence of nonzero terms. If x = (xk}∞k=0is any sequence of complex numbers we write Δ(m)x for the sequence of the m-th order differences of x and Δ(m)uX = {x = (x}∞k=0:uΔ(m)x ∈ X} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δ(m)uX for X = c0(p), c(p), l∞(p) and characterize some matrix transformations between these spaces Δ(m)X. © Springer-Verlag Berlin Heidelberg 2007. |
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Journal |
| author |
Eberhard Malkowsky Mursaleen Suthep Suantai |
| author_facet |
Eberhard Malkowsky Mursaleen Suthep Suantai |
| author_sort |
Eberhard Malkowsky |
| title |
The dual spaces of sets of difference sequences of order m and matrix transformations |
| title_short |
The dual spaces of sets of difference sequences of order m and matrix transformations |
| title_full |
The dual spaces of sets of difference sequences of order m and matrix transformations |
| title_fullStr |
The dual spaces of sets of difference sequences of order m and matrix transformations |
| title_full_unstemmed |
The dual spaces of sets of difference sequences of order m and matrix transformations |
| title_sort |
dual spaces of sets of difference sequences of order m and matrix transformations |
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2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=34047218579&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/61218 |
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