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Local completeness and dual local quasi-completeness

Authors:	Jinghui Qiu

Affiliation:	Department of Mathematics, Suzhou University, Suzhou 215006, People's Republic of China

Abstract:	It is proved that $l^{q}$ -completeness 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 -quasi-barrelledness are equivalent to each other.

Keywords:	Locally complete dual locally quasi-complete Banach-Mackey property quasi-Mackey spaces

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