Almost constrained subspaces of Banach spaces

A normed space is said to have ball-covering property if its unit sphere can be contained in the union of countably many open balls off the origin. This paper shows that for every ε > 0 every Banach space with a w * -separable dual has a 1+ε-equivalent norm with the ball covering property.Citation: Cheng L X, Shi H H, Zhang W. Every Banach space with a w * -separable dual has a 1 + ε-equivalent norm with the ball covering property.

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Almost constrained subspaces of Banach spaces

Abstract: Abstract. In this paper, we obtain some sufficient conditions for an almost constrained subspace to be constrained (in fact, by a unique norm 1 projection), which improves significantly upon all existing conditions of similar type with significantly simpler proofs.

Cited by 7 publications

References 21 publications

Vector valued invariant means, complementability and almost constrained subspaces

Vector valued invariant means, complementability and almost constrained subspaces

Optimal and one-complemented subspaces

Every Banach space with a w *-separable dual has a 1+ɛ-equivalent norm with the ball covering property

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