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Local completeness and dual local quasi-completeness


Author: Jinghui Qiu
Journal: Proc. Amer. Math. Soc. 129 (2001), 1419-1425
MSC (2000): Primary 46A08
DOI: https://doi.org/10.1090/S0002-9939-00-05717-8
Published electronically: October 24, 2000
MathSciNet review: 1814168
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Abstract:

It is proved that $l^{q}$-completeness $(1<q<\infty)$ is equivalent to $l^{1}$-completeness (defined by Saxon and Sánchez Ruiz), and becomes a new characteristic condition for local completeness. The relationship between dual local completeness, dual local quasi-completeness and the Banach-Mackey property is investigated. For a quasi-Mackey space, dual local quasi-completeness, $c_{0}$-quasi-barrelledness, Ruess' property (quasi-L) and $C$-quasi-barrelledness are equivalent to each other.


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Additional Information

Jinghui Qiu
Affiliation: Department of Mathematics, Suzhou University, Suzhou 215006, People’s Republic of China

DOI: https://doi.org/10.1090/S0002-9939-00-05717-8
Keywords: Locally complete, dual locally quasi-complete, Banach-Mackey property, quasi-Mackey spaces
Received by editor(s): September 28, 1998
Received by editor(s) in revised form: August 17, 1999
Published electronically: October 24, 2000
Communicated by: Dale E. Alspach
Article copyright: © Copyright 2000 American Mathematical Society

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