1,519,076 research outputs found
Coarse version of the Banach-Stone theorem
We show that if there exists a Lipschitz homeomorphism between the nets
in the Banach spaces and of continuous real valued functions on
compact spaces and , then the spaces and are homeomorphic
provided . By and we denote the
Lipschitz constants of the maps and . This improves the classical
result of Jarosz and the recent result of Dutrieux and Kalton where the
constant obtained is 17/16. We also estimate the distance of the map from
the isometry of the spaces and
Kazhdan and Haagerup properties from the median viewpoint
We prove the existence of a close connection between spaces with measured
walls and median metric spaces. We then relate properties (T) and Haagerup
(a-T-menability) to actions on median spaces and on spaces with measured walls.
This allows us to explore the relationship between the classical properties (T)
and Haagerup and their versions using affine isometric actions on -spaces.
It also allows us to answer an open problem on a dynamical characterization of
property (T), generalizing results of Robertson-Steger.Comment: final versio
The quest for the ultimate anisotropic Banach space
We present a new scale (with and ) of
anisotropic Banach spaces, defined via Paley-Littlewood, on which the transfer
operator associated to a hyperbolic dynamical system has good spectral
properties. When and is an integer, the spaces are analogous to the
"geometric" spaces considered by Gou\"ezel and Liverani. When and
, the spaces are somewhat analogous to the geometric
spaces considered by Demers and Liverani. In addition, just like for the
"microlocal" spaces defined by Baladi-Tsujii, the spaces are
amenable to the kneading approach of Milnor-Thurson to study dynamical
determinants and zeta functions.
In v2, following referees' reports, typos have been corrected (in particular
(39) and (43)). Section 4 now includes a formal statement (Theorem 4.1) about
the essential spectral radius if (its proof includes the content of
Section 4.2 from v1). The Lasota-Yorke Lemma 4.2 (Lemma 4.1 in v1) includes the
claim that is compact.
Version v3 contains an additional text "Corrections and complements" showing
that s> t-(r-1) is needed in Section 4.Comment: 31 pages, revised version following referees' reports, with
Corrections and complement
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