Strongly Bounded Partial Sums
If λ is a scalar sequence space, a series P Zj in a topological vector space Z is λ multiplier convergent in Z if the series P ∞J =1 tj Zj converges in Z for every t = {tj} ∈ λ-If λ satisfies appropriate conditions, a series in a locally convex...
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| Lenguaje: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2014
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| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000200006 |
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oai:scielo:S0716-091720140002000062018-10-30Strongly Bounded Partial SumsSwartz,CharlesIf λ is a scalar sequence space, a series P Zj in a topological vector space Z is λ multiplier convergent in Z if the series P ∞J =1 tj Zj converges in Z for every t = {tj} ∈ λ-If λ satisfies appropriate conditions, a series in a locally convex space X which is λ multiplier convergent in the weak topology is λ multiplier convergent in the original topology ofthe space (the Orlicz-Pettis Theorem) but may fail to be λ multiplier convergent in the strong topology of the space. However, we show under apprpriate conditions on the multiplier space λ that the series will have strongly bounded partial sums.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.33 n.2 20142014-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000200006en10.4067/S0716-09172014000200006 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| description |
If λ is a scalar sequence space, a series P Zj in a topological vector space Z is λ multiplier convergent in Z if the series P ∞J =1 tj Zj converges in Z for every t = {tj} ∈ λ-If λ satisfies appropriate conditions, a series in a locally convex space X which is λ multiplier convergent in the weak topology is λ multiplier convergent in the original topology ofthe space (the Orlicz-Pettis Theorem) but may fail to be λ multiplier convergent in the strong topology of the space. However, we show under apprpriate conditions on the multiplier space λ that the series will have strongly bounded partial sums. |
| author |
Swartz,Charles |
| spellingShingle |
Swartz,Charles Strongly Bounded Partial Sums |
| author_facet |
Swartz,Charles |
| author_sort |
Swartz,Charles |
| title |
Strongly Bounded Partial Sums |
| title_short |
Strongly Bounded Partial Sums |
| title_full |
Strongly Bounded Partial Sums |
| title_fullStr |
Strongly Bounded Partial Sums |
| title_full_unstemmed |
Strongly Bounded Partial Sums |
| title_sort |
strongly bounded partial sums |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2014 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000200006 |
| work_keys_str_mv |
AT swartzcharles stronglyboundedpartialsums |
| _version_ |
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