Displaying similar documents to “Weak Convergence and Weak Convergence”

The weak Phillips property

Ali Ülger (2001)

Colloquium Mathematicae

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Let X be a Banach space. If the natural projection p:X*** → X* is sequentially weak*-weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.

A new proof of James' sup theorem.

Marianne Morillon (2005)

Extracta Mathematicae

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We provide a new proof of James' sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnson: .

Topological Properties of Real Normed Space

Kazuhisa Nakasho, Yuichi Futa, Yasunari Shidama (2014)

Formalized Mathematics

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In this article, we formalize topological properties of real normed spaces. In the first part, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. Then we discuss linear functions between real normed speces. Several kinds of subspaces induced by linear functions such as kernel, image and inverse image are considered here. The fact that Lipschitz continuity operators preserve convergence of sequences...