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Projections in Weakly Compactly Generated Banach Spaces and Chang's Conjecture
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P. Koszmider
Published/Copyright:
June 9, 2010
Abstract
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 subspaces (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 (Pα : ω ≤ α ≤ λ) such that any projection is the sum of an operator in the closure of the linear span of countably many Pα's (in the strong operator topology) and a separable range operator. Wark's modification of Shelah's and Steprāns' construction provides an unconditional example for λ = ω1. We note that it is impossible for λ > ω2.
Received: 2003-05-28
Revised: 2004-09-26
Published Online: 2010-06-09
Published in Print: 2005-December
© Heldermann Verlag
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Keywords for this article
Weakly compactly generated Banach spaces;
Chang's conjecture;
few operators
Articles in the same Issue
- On Additive Almost Continuous Functions Under
- Maximal Solutions and Existence Theory for Fuzzy Differential and Integral Equations
- Projections in Weakly Compactly Generated Banach Spaces and Chang's Conjecture
- Dominated Convergence and Stone-Weierstrass Theorem
- Optimality Conditions and Duality for Multiobjective Control Problems
- On the Convergence of Sequences of Functions which are Discontinuous on Countable Sets
- Euler-Poincaré Formalism of Coupled KdV Type Systems and Diffeomorphism Group on S1
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