We construct an indecomposable reflexive Banach space such that every infinite-dimensional closed subspace contains an unconditional basic sequence. We also show that every operator is of the form λI + S with S a strictly singular operator.
We present a characterization of continuous surjections, between compact metric spaces, admitting a regular averaging operator. Among its consequences, concrete continuous surjections from the Cantor set 𝓒 to [0,1] admitting regular averaging operators are exhibited. Moreover we show that the set of this type of continuous surjections from 𝓒 to [0,1] is dense in the supremum norm in the set of all continuous surjections. The non-metrizable case is also investigated. As a consequence, we obtain...
It is shown that for every k ∈ ℕ and every spreading sequence eₙₙ that generates a uniformly convex Banach space E, there exists a uniformly convex Banach space admitting eₙₙ as a k+1-iterated spreading model, but not as a k-iterated one.
It is shown that every separable reflexive Banach space is a quotient of a reflexive hereditarily indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably -saturated space with and of a saturated space.
We present an example of a Banach space admitting an equivalent weakly uniformly rotund norm and such that there is no , for any set , linear, one-to-one and bounded. This answers a problem posed by Fabian, Godefroy, Hájek and Zizler. The space is actually the dual space of a space which is a subspace of a WCG space.
Page 1