Banach spaces with weak*-sequential dual ball
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- by Gonzalo Martínez-Cervantes PDF
- Proc. Amer. Math. Soc. 146 (2018), 1825-1832 Request permission
Abstract:
A topological space is said to be sequential if every subspace closed under taking limits of convergent sequences is closed. We consider Banach spaces with weak*-sequential dual ball. In particular, we show that if $X$ is a Banach space with weak*-sequentially compact dual ball and $Y \subset X$ is a subspace such that $Y$ and $X/Y$ have weak*-sequential dual ball, then $X$ has weak*-sequential dual ball. As an application we obtain that the Johnson-Lindenstrauss space $JL_2$ and $C(K)$ for $K$ a scattered compact space of countable height are examples of Banach spaces with weak*-sequential dual ball. These results provide a negative solution to a question of A. Plichko, who asked whether the dual ball of a Banach space is weak*-angelic whenever it is weak*-sequential.References
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Additional Information
- Gonzalo Martínez-Cervantes
- Affiliation: Departamento de Matemáticas, Facultad de Matemáticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain
- Email: gonzalo.martinez2@um.es
- Received by editor(s): December 19, 2016
- Received by editor(s) in revised form: May 17, 2017
- Published electronically: November 10, 2017
- Additional Notes: The author was partially supported by the research project 19275/PI/14 funded by Fundación Séneca - Agencia de Ciencia y Tecnología de la Región de Murcia within the framework of PCTIRM 2011-2014 and by Ministerio de Economía y Competitividad and FEDER (project MTM2014-54182-P)
- Communicated by: Thomas Schlumprecht
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1825-1832
- MSC (2010): Primary 57N17, 54D55, 46A50; Secondary 46B20, 46B50
- DOI: https://doi.org/10.1090/proc/13843
- MathSciNet review: 3754364