Vector measure Banach spaces containing a complemented copy of $c_{0}$
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- by A. Picón and C. Piñeiro PDF
- Proc. Amer. Math. Soc. 132 (2004), 2893-2898 Request permission
Abstract:
Let $X$ a Banach space and $\Sigma$ a $\sigma$-algebra of subsets of a set $\Omega$. We say that a vector measure Banach space $(\mathcal {M} (\Sigma , X ) , \Vert \cdot \Vert _\mathcal {M })$ has the bounded Vitaly-Hahn-Sacks Property if it satisfies the following condition: Every vector measure $m : \Sigma \longrightarrow X$ , for which there exists a bounded sequence $(m_{n})$ in $\mathcal {M } (\Sigma , X )$ verifying $\displaystyle \lim _{n \to \infty } m_{n} ( A ) = m(A)$ for all $A \in \Sigma$, must belong to $\mathcal {M} (\Sigma , X)$. Among other results, we prove that, if $\mathcal {M}(\Sigma , X)$ is a vector measure Banach space with the bounded V-H-S Property and containing a complemented copy of $c_{0}$, then $X$ contains a copy of $c_{0}$.References
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Additional Information
- A. Picón
- Affiliation: Departamento de Matemáticas, Facultad de Ciencias Experimentales, Campus universitario de El Carmen, Universidad de Huelva, 21071, Huelva, Spain
- C. Piñeiro
- Affiliation: Departamento de Matemáticas, Facultad de Ciencias Experimentales, Campus universitario de El Carmen, Universidad de Huelva, 21071, Huelva, Spain
- Email: candido@uhu.es
- Received by editor(s): May 14, 2002
- Published electronically: May 21, 2004
- Communicated by: Jonathan M. Borwein
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2893-2898
- MSC (2000): Primary 46G10
- DOI: https://doi.org/10.1090/S0002-9939-04-07518-5
- MathSciNet review: 2063108