Book Review: Schauder bases in Banach spaces of continuous functions

Fractal Functions and Schauder Bases

1. Introduction. In recent years more and more attention has been paid in mathematical papers to fractal functions and to fractal sets. There are various definitions of those objects. We assume that a compact set K ∈ R d+1 is fractal, by definition, if its box (entropy) dimension dim b (K) = j for j = 0, 1,. .. , d + 1 and 0 < dim b (K) < d + 1. At the same time the function f : I d → R d , I =...

On Bases in Banach Spaces

We investigate various kinds of bases in infinite dimensional Banach spaces. In particular, we consider the complexity of Hamel bases in separable and non-separable Banach spaces and show that in a separable Banach space a Hamel basis cannot be analytic, whereas there are non-separable Hilbert spaces which have a discrete and closed Hamel basis. Further we investigate the existence of certain c...

Uniqueness of Unconditional Bases in Banach Spaces

We prove a general result on complemented unconditional basic sequences in Banach lattices and apply it to give some new examples of spaces with unique unconditional basis. We show that Tsirelson space and certain Nakano spaces have unique unconditional bases. We also construct an example of a space with a unique unconditional basis with a complemented subspace failing to have a unique uncondit...

L−maximal Regularity on Banach Spaces with a Schauder Basis

We investigate the problem of L p-maximal regularity on Ba-nach spaces having a Schauder basis. Our results improve those of a recent paper.

Spaces of continuous functions into a Banach space