Linearizability of Non-expansive Semigroup Actions on Metric Spaces (bibtex)

by Lutz Schröder

Abstract:

We show that a non-expansive action of a topological semigroup S on a metric space X is linearizable iff its orbits are bounded. The crucial point here is to prove that X can be extended by adding a fixed point of S, thus allowing application of a semigroup version of the Arens-Eells linearization, iff the orbits of S in X are bounded.

Reference:

Lutz Schröder: Linearizability of Non-expansive Semigroup Actions on Metric Spaces, In Topology and its Applications, 155, pp. 1576–1579, 2008. Preliminary version appeared as DFKI Research Report RR-06-1, DFKI GmbH, Kaiserslautern, 2006 [preprint]

Bibtex Entry:

@Article{Schroder07b,
  author = {Lutz Schr{\"o}der},
  title = {Linearizability of Non-expansive Semigroup Actions on Metric Spaces},
  year = {2008},
  journal = {Topology and its Applications},
  volume = {155},
  pages = {1576-1579},
  keywords = {Metric space semigroup action fixed point linearization},
  comment = { <a href = "http://www8.informatik.uni-erlangen.de/~schroeder/papers/FixedPoint.pdf"> [preprint] </a>},
  abstract = {We show that a non-expansive action of a topological semigroup S on a
metric space X is linearizable iff its orbits are bounded. The crucial
point here is to prove that X can be extended by adding a fixed point
of S, thus allowing application of a semigroup version of the
Arens-Eells linearization, iff the orbits of S in X are bounded.
},
  note = {Preliminary version appeared as <a href="http://www8.informatik.uni-erlangen.de/~schroeder/papers/RRFixedPoint.pdf">DFKI Research Report RR-06-1</a>, DFKI GmbH, Kaiserslautern, 2006},
}