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A weak* approximation of subgradient of convex function

Zagrodny D.

Control and Cybernetics

2007

Vol. 36, no. 3

793-802

Let [...] be a sequence of proper lower semicontinuous convex functions on a weakly compactly generated Banach space. Conditions ensuring the weak* convergence of their subgradients are given.

Projections in weakly compactly generated Banach spaces and Chang's conjecture

Koszmider P.

Journal of Applied Analysis

2005

Vol. 11, nr 2

187-205

Classical results on weakly compactly generated (WCG) Banach spaces imply the existence of projectional resolutions of identity (PRI) and the existence of many projections on separable sub-spaces (SCP). We address the questions if these can be the only projections in a nonseparable WCG space, in the sense that there is a PRI [wzór] such that any projection is the sum of an operator in the closure of the linear span of countably many P ∝'s (in the strong operator topology) and a separable range operator. Wark's modification of Shelah's and Steprans' construction provides an unconditional example for λ ω 2. We note that it is impossible for λ > ω 2.