Polyhedral norms on non-separable Banach spaces

Analytic approximations of norms in separable Banach spaces

Evolution inclusions in non separable Banach spaces

We study a Cauchy problem for non-convex valued evolution inclusions in non separable Banach spaces under Filippov type assumptions. We establish existence and relaxation theorems.

Non - separable Banach spaces with non - meager Hamel basis

We show that an infinite-dimensional complete linear space X has: • a dense hereditarily Baire Hamel basis if |X| ≤ c; • a dense non-meager Hamel basis if |X| = κ = 2 for some cardinal κ. According to Corollary 3.4 of [BDHMP] each infinite-dimensional separable Banach space X has a non-meager Hamel basis. This is a special case of Theorem3.3 of [BDHMP], asserting that an infinite-dimensional Ba...

Lfc Bumps on Separable Banach Spaces

In this note we construct a C∞-smooth, LFC (Locally depending on Finitely many Coordinates) bump function, in every separable Banach space admitting a continuous, LFC bump function.

Non Dentable Sets in Banach Spaces with Separable Dual

A non RNP Banach space E is constructed such that E∗ is separable and RNP is equivalent to PCP on the subsets of E. The problem of the equivalence of the Radon-Nikodym Property (RNP) and the Krein Milman Property (KMP) remains open for Banach spaces as well as for closed convex sets. A step forward has been made by Schachermayer’s Theorem [S]. That result states that the two properties are equi...