TY - JOUR

T1 - Hölder Continuity for the Inverse of Mañé′s Projection

AU - Ben-Artzi, A.

AU - Eden, A.

AU - Foias, C.

AU - Nicolaenko, B.

PY - 1993/9/1

Y1 - 1993/9/1

N2 - In a celebrated work, Mañé showed that given a compact set X with fractal dimension d in a Banach space B, there exists a projection P of rank ≤2d + 1, such that P restricted to X is injective. Here, we prove a stronger result when B is finite dimensional, namely, that there exists an orthogonal projection P0 such that not only P0 is injective on X but also its inverse is Hölder continuous when restricted to P0X.

AB - In a celebrated work, Mañé showed that given a compact set X with fractal dimension d in a Banach space B, there exists a projection P of rank ≤2d + 1, such that P restricted to X is injective. Here, we prove a stronger result when B is finite dimensional, namely, that there exists an orthogonal projection P0 such that not only P0 is injective on X but also its inverse is Hölder continuous when restricted to P0X.

UR - http://www.scopus.com/inward/record.url?scp=0002140877&partnerID=8YFLogxK

U2 - 10.1006/jmaa.1993.1288

DO - 10.1006/jmaa.1993.1288

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AN - SCOPUS:0002140877

SN - 0022-247X

VL - 178

SP - 22

EP - 29

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -