Projecting Lipschitz functions onto spaces of polynomials

0559509 - MÚ 2023 RIV CH eng J - Journal Article
Hájek, P. - Russo, Tommaso
Projecting Lipschitz functions onto spaces of polynomials.
Mediterranean Journal of Mathematics. Roč. 19, č. 4 (2022), č. článku 190. ISSN 1660-5446. E-ISSN 1660-5454
R&D Projects: GA ČR(CZ) GF20-22230L
Institutional support: RVO:67985840
Keywords : Banach spaces of Lipschitz functions * complemented subspaces * Euclidean spaces * polynomials * type and cotype
OECD category: Pure mathematics
Impact factor: 1.1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1007/s00009-022-02075-6

The Banach space P(2X) of 2-homogeneous polynomials on the Banach space X can be naturally embedded in the Banach space Lip (BX) of real-valued Lipschitz functions on BX that vanish at 0. We investigate whether P(2X) is a complemented subspace of Lip (BX). This line of research can be considered as a polynomial counterpart to a classical result by Joram Lindenstrauss, asserting that P(1X) = X∗ is complemented in Lip (BX) for every Banach space X. Our main result asserts that P(2X) is not complemented in Lip (BX) for every Banach space X with non-trivial type.
Permanent Link: https://hdl.handle.net/11104/0332786