JEDNOSTKA NAUKOWA KATEGORII A+

Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

Perturbations of isometries between Banach spaces

Tom 207 / 2011

Studia Mathematica 207 (2011), 47-58 MSC: 46E40, 46B20. DOI: 10.4064/sm207-1-3

Streszczenie

We prove a very general theorem concerning the estimation of the expression $\|T(\frac{a+b}{2}) - \frac{Ta+Tb}{2}\|$ for different kinds of maps $T$ satisfying some general perturbed isometry condition. It can be seen as a quantitative generalization of the classical Mazur–Ulam theorem. The estimates improve the existing ones for bi-Lipschitz maps. As a consequence we also obtain a very simple proof of the result of Gevirtz which answers the Hyers–Ulam problem and we prove a non-linear generalization of the Banach–Stone theorem which improves the results of Jarosz and more recent results of Dutrieux and Kalton.

Autorzy

• Rafał GórakTechnical University of Warsaw
Pl. Politechniki 1
00-661 Warszawa, Poland
e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek