TY - JOUR
T1 - Every Semitopological Semigroup Compactification of the Group H+[0, 1] is Trivial
AU - Megrelishvili, Michael G.
PY - 2001
Y1 - 2001
N2 - Let G = H+[0, 1] be the topological group of all orientation-preserving selfhomeomorphisms of the closed interval [0, 1] endowed with the usual compact open topology. We show that every weakly almost periodic function on G is constant. Consequently, G does not admit nontrivial (weakly) continuous representations by linear isometries in reflexive Banach spaces.
AB - Let G = H+[0, 1] be the topological group of all orientation-preserving selfhomeomorphisms of the closed interval [0, 1] endowed with the usual compact open topology. We show that every weakly almost periodic function on G is constant. Consequently, G does not admit nontrivial (weakly) continuous representations by linear isometries in reflexive Banach spaces.
KW - Semitopological semigroup compactification
KW - Weakly almost periodic function
UR - http://www.scopus.com/inward/record.url?scp=0041330539&partnerID=8YFLogxK
U2 - 10.1007/s002330010076
DO - 10.1007/s002330010076
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AN - SCOPUS:0041330539
SN - 0037-1912
VL - 63
SP - 357
EP - 370
JO - Semigroup Forum
JF - Semigroup Forum
IS - 3
ER -