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 -