On a problem of Fell and Doran
In this short article we answer the question posed in Ghadermazi M., Karamzadeh O.A.S., Namdari M., On the functionally countable subalgebra of , Rend. Sem. Mat. Univ. Padova 129 (2013), 47–69. It is shown that is isomorphic to some ring of continuous functions if and only if is functionally countable. For a strongly zero-dimensional space , this is equivalent to say that is functionally countable. Hence for every -space it is equivalent to pseudo--compactness.
The present paper deals with a question of M. Mbekhta concerning partial isometries on Banach spaces.
We exhibit new examples of weakly compact strictly singular operators with dual not strictly cosingular and characterize the weakly compact strictly singular surjections with strictly cosingular adjoint as those having strictly singular bitranspose. We then obtain new examples of super-strictly singular quotient maps and show that the strictly singular quotient maps in Kalton-Peck sequences are not super-strictly singular.
Let Ω be a nonatomic probability space, let X be a Banach function space over Ω, and let ℳ be the collection of all martingales on Ω. For , let Mf and Sf denote the maximal function and the square function of f, respectively. We give some necessary and sufficient conditions for X to have the property that if f, g ∈ ℳ and , then , where C is a constant independent of f and g.