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A characterization of regular averaging operators and its consequences

100%
Argyros S., Arvanitakis A.
Studia Mathematica
|
2002
|
tom 151
|
nr 3
207-226
EN
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 a new characterization of Eberlein compact sets.
2
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Examples of k-iterated spreading models

100%
Argyros S., Motakis P.
Studia Mathematica
|
2013
|
tom 217
|
nr 1
57-78
EN
It is shown that for every k ∈ ℕ and every spreading sequence {eₙ}ₙ that generates a uniformly convex Banach space E, there exists a uniformly convex Banach space $X_{k+1}$ admitting {eₙ}ₙ as a k+1-iterated spreading model, but not as a k-iterated one.
3
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An indecomposable and unconditionally saturated Banach space

100%
Argyros S., Manoussakis A.
Studia Mathematica
|
2003
|
tom 159
|
nr 1
1-32
EN
We construct an indecomposable reflexive Banach space $X_{ius}$ such that every infinite-dimensional closed subspace contains an unconditional basic sequence. We also show that every operator $T ∈ ℬ (X_{ius})$ is of the form λI + S with S a strictly singular operator.
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