This is an announcement for the paper "Examples and counterexamples of type I isometric shifts" by Jesus Araujo.
Abstract: We provide examples of nonseparable spaces $X$ for which $C(X)$ admits an isometric shift of type I, which solves in the negative a problem proposed by Gutek {\em et al.} (J. Funct. Anal. {\bf 101} (1991), 97-119). We also give two independent methods for obtaining separable examples. The first one allows us in particular to construct examples with infinitely many nonhomeomorphic components in a subset of the Hilbert space $\ell^2$. The second one applies for instance to sequences adjoined to any $n$-dimensional compact manifold (for $n \ge 2$) or to the Sierpi'nski curve. The combination of both techniques lead to different examples involving a convergent sequence adjoined to the Cantor set: one method for the case when the sequence converges to a point in the Cantor set, and the other one for the case when it converges outside.
Archive classification: Functional Analysis; General Topology
Mathematics Subject Classification: Primary 47B38; Secondary 46E15, 47B33, 47B37, 54D65, 54H20
Remarks: 41 pages. No figures. AMS-LaTeX
The source file(s), shiftnum86.tex: 124237 bytes, is(are) stored in gzipped form as 0703892.gz with size 34kb. The corresponding postcript file has gzipped size 210kb.
Submitted from: araujoj@unican.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0703892
or
http://arXiv.org/abs/math.FA/0703892
or by email in unzipped form by transmitting an empty message with subject line
uget 0703892
or in gzipped form by using subject line
get 0703892
to: math@arXiv.org.