# [Banach] Abstract of a paper by Jesus Araujo

Dale Alspach alspach at www.math.okstate.edu
Tue Apr 10 07:03:19 CDT 2007

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 at unican.es

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http://front.math.ucdavis.edu/math.FA/0703892

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http://arXiv.org/abs/math.FA/0703892

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