Reflexively representable but not Hilbert representable compact flows and semitopological semigroups

• Autorzy: Michael Megrelishvili
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 54H20: Topological dynamics
• 43A65: Representations of groups, semigroups, etc.
• 54H15: Transformation groups and semigroups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 110
• Numer: 2
• Strony: 383-407

Daty

wydano

2008

Twórcy

autor

Michael Megrelishvili

• Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel

Identyfikatory

DOI

10.4064/cm110-2-5