Search results for " 46B85"

showing 2 items of 2 documents

Isometric embeddings of snowflakes into finite-dimensional Banach spaces

2016

We consider a general notion of snowflake of a metric space by composing the distance by a nontrivial concave function. We prove that a snowflake of a metric space $X$ isometrically embeds into some finite-dimensional normed space if and only if $X$ is finite. In the case of power functions we give a uniform bound on the cardinality of $X$ depending only on the power exponent and the dimension of the vector space.

30L05 46B85 54C25 54E40 28A80Pure mathematicsmetric spacesGeneral MathematicsMathematicsofComputing_GENERALBanach space01 natural sciencesfunctional analysisCardinalityMathematics - Metric GeometryDimension (vector space)0103 physical sciencesFOS: MathematicsMathematics (all)Mathematics::Metric Geometry0101 mathematicsSnowflakeNormed vector spaceMathematicsConcave functionApplied Mathematicsta111010102 general mathematicsnormiavaruudetMetric Geometry (math.MG)normed spacesmetriset avaruudetMetric spacefractalsfraktaalit010307 mathematical physicsfunktionaalianalyysiMathematics (all); Applied MathematicsVector spaceProceedings of the American Mathematical Society
researchProduct

SPACES OF SMALL METRIC COTYPE

2010

Naor and Mendel's metric cotype extends the notion of the Rademacher cotype of a Banach space to all metric spaces. Every Banach space has metric cotype at least 2. We show that any metric space that is bi-Lipschitz equivalent to an ultrametric space has infinimal metric cotype 1. We discuss the invariance of metric cotype inequalities under snowflaking mappings and Gromov-Hausdorff limits, and use these facts to establish a partial converse of the main result.

Mathematics::Functional AnalysisPure mathematics30L05 46B85010102 general mathematicsBanach spaceMetric Geometry (math.MG)0102 computer and information sciences16. Peace & justice01 natural sciencesFunctional Analysis (math.FA)Mathematics - Functional AnalysisMetric spaceMathematics - Metric Geometry010201 computation theory & mathematicsConverseMetric (mathematics)FOS: MathematicsMathematics::Metric GeometryGeometry and Topology0101 mathematicsIsoperimetric inequalityUltrametric spaceAnalysisMathematicsJournal of Topology and Analysis
researchProduct