Reflexively representable but not Hilbert representable compact flows and semitopological semigroups

Michael Megrelishvili. "Reflexively representable but not Hilbert representable compact flows and semitopological semigroups." Colloquium Mathematicae 110.2 (2008): 383-407. <http://eudml.org/doc/284329>.

@article{MichaelMegrelishvili2008,
abstract = {We show that for many natural topological groups G (including the group ℤ of integers) there exist compact metric G-spaces (cascades for G = ℤ) which are reflexively representable but not Hilbert representable. This answers a question of T. Downarowicz. The proof is based on a classical example of W. Rudin and its generalizations. A~crucial step in the proof is our recent result which states that every weakly almost periodic function on a compact G-flow X comes from a G-representation of X on reflexive spaces. We also show that there exists a monothetic compact metrizable semitopological semigroup S which does not admit an embedding into the semitopological compact semigroup Θ(H) of all contractive linear operators on a Hilbert space H (though S admits an embedding into the compact semigroup Θ(V) for certain reflexive V).},
author = {Michael Megrelishvili},
journal = {Colloquium Mathematicae},
keywords = {semitopological semigroup; enveloping semigroup; weakly almost periodic compactification; matrix coefficient; Fourier-Stieltjes algebra},
language = {eng},
number = {2},
pages = {383-407},
title = {Reflexively representable but not Hilbert representable compact flows and semitopological semigroups},
url = {http://eudml.org/doc/284329},
volume = {110},
year = {2008},
}

TY - JOUR
AU - Michael Megrelishvili
TI - Reflexively representable but not Hilbert representable compact flows and semitopological semigroups
JO - Colloquium Mathematicae
PY - 2008
VL - 110
IS - 2
SP - 383
EP - 407
AB - We show that for many natural topological groups G (including the group ℤ of integers) there exist compact metric G-spaces (cascades for G = ℤ) which are reflexively representable but not Hilbert representable. This answers a question of T. Downarowicz. The proof is based on a classical example of W. Rudin and its generalizations. A~crucial step in the proof is our recent result which states that every weakly almost periodic function on a compact G-flow X comes from a G-representation of X on reflexive spaces. We also show that there exists a monothetic compact metrizable semitopological semigroup S which does not admit an embedding into the semitopological compact semigroup Θ(H) of all contractive linear operators on a Hilbert space H (though S admits an embedding into the compact semigroup Θ(V) for certain reflexive V).
LA - eng
KW - semitopological semigroup; enveloping semigroup; weakly almost periodic compactification; matrix coefficient; Fourier-Stieltjes algebra
UR - http://eudml.org/doc/284329
ER -