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Normed barrelled spaces

Christopher Stuart — 2000

Banach Center Publications

In this paper we present a general “gliding hump” condition that implies the barrelledness of a normed vector space. Several examples of subspaces of $l^{1}$ are shown to be barrelled using the theorem. The barrelledness of the space of Pettis integrable functions is also implied by the theorem (this was first shown in [3]).

A generalization of the Nikodym boundedness theorem.

Christopher Stuart — 2007

Collectanea Mathematica

In this note an internal property of a ring of sets, named the Nested Partition Property, is shown to imply the Nikodym Property. A wide range of examples are shown to have this property.

A projection property and weak sequential completeness of alfa-duals.

Charles Swartz; Christopher Stuart — 1992

Collectanea Mathematica

Dense barrelled subspace of Banach spaces.

Christopher E. Stuart — 1996

Collectanea Mathematica

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