A space C(K) where all nontrivial complemented subspaces have big densities

A construction of a Banach space C(K) with few operators

“…his preprints [16,17] available, as well as for the correspondence concerning his results. I thank Mirna Džamonja for very stimulating discussions on lattices and representation theorems, in particular for her notes [7] extracting some interesting ideas from Jung and Sȗnderhauf [14]; they were very helpful though not directly reflected in our present approach.…”

Proximinality and Diametrically Maximal Sets in $C(K)$

“…We are concerned in this paper with the following Problem P : given C ∈ M, Minimize dist(C, E) subject to E ∈ γ(C) and the corresponding Problem P ′ obtained by replacing the above constraint by the weaker restriction E ∈ DM. Though spaces of continuous functions often present a variety of behaviors (actually they are often used as a source of counterexamples [13]), both problems have optimal solutions in every C(K) space. We will provide a characterization of the uniqueness of the optimal solutions in Problem P.…”

Construções consistentes de espaços de Banach C (K) com poucos operadores

“…A próxima afirmaçãoé uma adaptação para o caso não 0-dimensional de parte da demonstração do Lema 7 de [Ko3]. Notamos que, se A n 's são abertos-fechados, ∆((A n ) n∈ω ) = n∈ω A n − n∈ω A n , conforme o enunciado do Lema 7 de [Ko3].…”

“…Notamos que, se A n 's são abertos-fechados, ∆((A n ) n∈ω ) = n∈ω A n − n∈ω A n , conforme o enunciado do Lema 7 de [Ko3].…”

“…Em [Ko3] foi mostrado que existe consistentemente C(K) de densidade maior que contínuo com poucos operadores. Porém ainda não sabemos se existe C(K) indecomponível de densidade maior que contínuo.…”