Metric projections after renorming

Metrizability of Cone Metric Spaces Via Renorming the Banach Spaces

In this paper we show that by renorming an ordered Banach space, every cone P can be converted to a normal cone with constant K = 1 and consequently due to this approach every cone metric space is really a metric one and every theorem in metric space is valid for cone metric space automatically.

On projections of metric spaces

Let X be a metric space and let μ be a probability measure on it. Consider a Lipschitz map T : X → Rn, with Lipschitz constant ≤ 1. Then one can ask whether the image TX can have large projections on many directions. For a large class of spaces X, we show that there are directions φ ∈ Sn−1 on which the projection of the image TX is small on the average (in L2(μ)), with bounds depending on the d...

Renorming James Tree Space

We show that James tree space JT can be renormed to be Lipschitz separated. It negatively answers the question of J. Borwein, J. Giles and J. Vanderwerff whether every Lipschitz separated Banach space is an Asplund space.

Trees in Renorming Theory

Some New Continuity Concepts for Metric Projections