Ben-Artzi, A.; Eden, A.; Foiaş, C.; Nicolaenko, B. Hölder continuity for the inverse of Mañé’s projection. (English) Zbl 0815.46016 J. Math. Anal. Appl. 178, No. 1, 22-29 (1993). In [Lect. Notes Math. 898, 230-242 (1981; Zbl 0544.58014)], R. Mañé showed that given a compact set \(X\) with fractal dimension \(d\) in a Banach space \(B\), there exists a projection \(P\) of rank \(\leq 2d+1\), such that \(P\) restricted to \(X\) is injective. Here, the authors prove a stronger result when \(B\) is finite dimensional, namely that there exists an orthogonal projection \(P_ 0\) such that not only \(P_ 0\) is injective on \(X\) but also its inverse is Hölder continuous when restricted to \(P_ 0 X\). Cited in 1 ReviewCited in 17 Documents MSC: 46B20 Geometry and structure of normed linear spaces 58C05 Real-valued functions on manifolds 46M10 Projective and injective objects in functional analysis Keywords:fractal dimension; orthogonal projection; Hölder continuous Citations:Zbl 0544.58014 PDFBibTeX XMLCite \textit{A. Ben-Artzi} et al., J. Math. Anal. Appl. 178, No. 1, 22--29 (1993; Zbl 0815.46016) Full Text: DOI