Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 6

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

On the non-existence of certain group topologies

100%
Rosendal C.
Fundamenta Mathematicae
|
2005
|
tom 187
|
nr 3
213-228
EN
Minimal Hausdorff (Baire) group topologies of certain groups of transformations naturally occurring in analysis are studied. The results obtained are subsequently applied to show that, e.g., the homeomorphism groups of the rational and of the irrational numbers carry no Polish group topology. In answer to a question of A. S. Kechris it is shown that the group of Borel automorphisms of ℝ cannot be a Polish group either.
2
Content available remote

Incomparable, non-isomorphic and minimal Banach spaces

100%
Rosendal C.
Fundamenta Mathematicae
|
2004
|
tom 183
|
nr 3
253-274
EN
A Banach space contains either a minimal subspace or a continuum of incomparable subspaces. General structure results for analytic equivalence relations are applied in the context of Banach spaces to show that if E₀ does not reduce to isomorphism of the subspaces of a space, in particular, if the subspaces of the space admit a classification up to isomorphism by real numbers, then any subspace with an unconditional basis is isomorphic to its square and hyperplanes, and the unconditional basis has an isomorphically homogeneous subsequence.
3
Content available remote

The generic isometry and measure preserving homeomorphism are conjugate to their powers

100%
Rosendal C.
Fundamenta Mathematicae
|
2009
|
tom 205
|
nr 1
1-27
EN
It is known that there is a comeagre set of mutually conjugate measure preserving homeomorphisms of Cantor space equipped with the coinflipping probability measure, i.e., Haar measure. We show that the generic measure preserving homeomorphism is moreover conjugate to all of its powers. It follows that the generic measure preserving homeomorphism extends to an action of (ℚ, +) by measure preserving homeomorphisms, and, in fact, to an action of the locally compact ring 𝔄 of finite adèles. Similarly, S. Solecki has proved that there is a comeagre set of mutually conjugate isometries of the rational Urysohn metric space. We prove that these are all conjugate with their powers and therefore also embed into ℚ-actions. In fact, we extend these actions to actions of 𝔄 as in the case of measure preserving homeomorphisms. We also consider a notion of topological similarity in Polish groups and use this to give simplified proofs of the meagreness of conjugacy classes in the automorphism group of the standard probability space and in the isometry group of the Urysohn metric space.
4
Content available remote

Determinacy of adversarial Gowers games

100%
Rosendal C.
Fundamenta Mathematicae
|
2014
|
tom 227
|
nr 2
163-178
EN
We prove a game-theoretic dichotomy for $G_{δσ}$ sets of block sequences in vector spaces that extends, on the one hand, the block Ramsey theorem of W. T. Gowers proved for analytic sets of block sequences and, on the other hand, M. Davis' proof of Σ⁰₃ determinacy.
5
Content available remote

Characterising subspaces of Banach spaces with a Schauder basis having the shift property

100%
Rosendal C.
Studia Mathematica
|
2011
|
tom 207
|
nr 1
59-73
EN
We give an intrinsic characterisation of the separable reflexive Banach spaces that embed into separable reflexive spaces with an unconditional basis all of whose normalised block sequences with the same growth rate are equivalent. This uses methods of E. Odell and T. Schlumprecht.
6
Content available remote

On the number of non-isomorphic subspaces of a Banach space

64%
Ferenczi V., Rosendal C.
Studia Mathematica
|
2005
|
tom 168
|
nr 3
203-216
EN
We study the number of non-isomorphic subspaces of a given Banach space. Our main result is the following. Let 𝔛 be a Banach space with an unconditional basis $(e_{i})_{i∈ℕ}$; then either there exists a perfect set P of infinite subsets of ℕ such that for any two distinct A,B ∈ P, $[e_{i}]_{i∈A} ≇ [e_{i}]_{i∈B}$, or for a residual set of infinite subsets A of ℕ, $[e_{i}]_{i∈A}$ is isomorphic to 𝔛, and in that case, 𝔛 is isomorphic to its square, to its hyperplanes, uniformly isomorphic to $𝔛 ⊕ [e_{i}]_{i∈D}$ for any D ⊂ ℕ, and isomorphic to a denumerable Schauder decomposition into uniformly isomorphic copies of itself.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.