Some results on the span of families of Banach valued independent, random variables
Let E be a Banach space, and let (Ω,ℱ,P) be a probability space. If L1(Ω) contains an isomorphic copy of L1[0,1] then in LEP(Ω)(1≤P<∞), the closed linear span of every sequence of independent, E valued mean zero random variables has infinite codimension. If E is reflexive or B-convex and 1<P&l...
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| Format: | Article |
| Language: | English |
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Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171291000443 |
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| _version_ | 1832548483260743680 |
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| author | Rohan Hemasinha |
| author_facet | Rohan Hemasinha |
| author_sort | Rohan Hemasinha |
| collection | DOAJ |
| description | Let E be a Banach space, and let (Ω,ℱ,P) be a probability space.
If L1(Ω) contains an isomorphic copy of L1[0,1] then in LEP(Ω)(1≤P<∞), the closed
linear span of every sequence of independent, E valued mean zero random variables has
infinite codimension. If E is reflexive or B-convex and 1<P<∞ then the closed
(in LEP(Ω)) linear span of any family of independent, E valued, mean zero random
variables is super-reflexive. |
| format | Article |
| id | doaj-art-a363d197c7af44de9319c18dc928da32 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a363d197c7af44de9319c18dc928da322025-02-03T06:14:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114238138410.1155/S0161171291000443Some results on the span of families of Banach valued independent, random variablesRohan Hemasinha0University of West Florida, Pensacola 32514, FL, USALet E be a Banach space, and let (Ω,ℱ,P) be a probability space. If L1(Ω) contains an isomorphic copy of L1[0,1] then in LEP(Ω)(1≤P<∞), the closed linear span of every sequence of independent, E valued mean zero random variables has infinite codimension. If E is reflexive or B-convex and 1<P<∞ then the closed (in LEP(Ω)) linear span of any family of independent, E valued, mean zero random variables is super-reflexive.http://dx.doi.org/10.1155/S0161171291000443Banach valued random variableunconditional basic sequence finite representabilitysuper-reflexive banach spaceB-convex banach space(n,δ)-tree. |
| spellingShingle | Rohan Hemasinha Some results on the span of families of Banach valued independent, random variables International Journal of Mathematics and Mathematical Sciences Banach valued random variable unconditional basic sequence finite representability super-reflexive banach space B-convex banach space (n,δ)-tree. |
| title | Some results on the span of families of Banach valued independent, random variables |
| title_full | Some results on the span of families of Banach valued independent, random variables |
| title_fullStr | Some results on the span of families of Banach valued independent, random variables |
| title_full_unstemmed | Some results on the span of families of Banach valued independent, random variables |
| title_short | Some results on the span of families of Banach valued independent, random variables |
| title_sort | some results on the span of families of banach valued independent random variables |
| topic | Banach valued random variable unconditional basic sequence finite representability super-reflexive banach space B-convex banach space (n,δ)-tree. |
| url | http://dx.doi.org/10.1155/S0161171291000443 |
| work_keys_str_mv | AT rohanhemasinha someresultsonthespanoffamiliesofbanachvaluedindependentrandomvariables |