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Reflexively representable but not Hilbert representable compact flows and semitopological semigroups

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Megrelishvili M.

Colloquium Mathematicum

2008

tom 110

nr 2

383-407

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).

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1 Colloquium Mathematicum

1 Megrelishvili M.

1 2008

Wyniki wyszukiwania

Reflexively representable but not Hilbert representable compact flows and semitopological semigroups