Absolute Lipschitz extendability and linear projection constants

نویسندگان

چکیده

We prove that the absolute extendability constant of a finite metric space may be determined by computing relative projection constants certain Lipschitz-free spaces. As an application, we show $\mbox{ae}(3)=4/3$ and $\mbox{ae}(4)\geq (5+4\sqrt{2})/7$. Moreover, discuss how to compute solving linear programming problems.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Absolute Lipschitz extendability

A metric space X is said to be absolutely Lipschitz extendable if every Lipschitz function f from X into any Banach space Z can be extended to any containing space Y ⊇ X , where the loss in the Lipschitz constant in the extension is independent of Y , Z, and f . We show that various classes of natural metric spaces are absolutely Lipschitz extendable. c © 2003 Académie des sciences/Éditions sci...

متن کامل

Lipschitz Extension Constants Equal Projection Constants

For a Banach space V we define its Lipschitz extension constant, LE(V ), to be the infimum of the constants c such that for every metric space (Z, ρ), every X ⊂ Z, and every f : X → V , there is an extension, g, of f to Z such that L(g) ≤ cL(f), where L denotes the Lipschitz constant. The basic theorem is that when V is finite-dimensional we have LE(V ) = PC(V ) where PC(V ) is the well-known p...

متن کامل

Minimal Projections and Absolute Projection Constants for Regular Polyhedral Spaces

Let V« [vx,...,vn] be the «-dimensional space of coordinate functions on a set of points ¡cR" where v is the set of vertices of a regular convex polyhedron. In this paper the absolute projection constant of any «-dimensional Banach space E isometrically isomorphic to V c C(v) is computed, examples of which are the well-known cases E = ITM, lln.

متن کامل

Projection Inequalities and Their Linear Preservers

This paper introduces an inequality on vectors in $mathbb{R}^n$ which compares vectors in $mathbb{R}^n$ based on the $p$-norm of their projections on $mathbb{R}^k$ ($kleq n$). For $p>0$, we say $x$ is $d$-projectionally less than or equal to $y$ with respect to $p$-norm if $sum_{i=1}^kvert x_ivert^p$ is less than or equal to $ sum_{i=1}^kvert y_ivert^p$, for every $dleq kleq n$. For...

متن کامل

Lipschitz Constants to Curve Complexes

We determine the asymptotic behavior of the optimal Lipschitz constant for the systole map from Teichmüller space to the curve complex.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Studia Mathematica

سال: 2022

ISSN: ['0039-3223', '1730-6337']

DOI: https://doi.org/10.4064/sm210708-21-9