Topologically Invertible Elements and Topological Spectrum

Mati Abel, and Wiesław Żelazko. "Topologically Invertible Elements and Topological Spectrum." Bulletin of the Polish Academy of Sciences. Mathematics 54.3 (2006): 257-271. <http://eudml.org/doc/280628>.

@article{MatiAbel2006,
abstract = {Properties of topologically invertible elements and the topological spectrum of elements in unital semitopological algebras are studied. It is shown that the inversion $x ↦ x^\{-1\}$ is continuous in every invertive Fréchet algebra, and singly generated unital semitopological algebras have continuous characters if and only if the topological spectrum of the generator is non-empty. Several open problems are presented.},
author = {Mati Abel, Wiesław Żelazko},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {topologically invertible elements; topological spectrum; spectral mapping property; discontinuity of inversion; functional topological spectrum},
language = {eng},
number = {3},
pages = {257-271},
title = {Topologically Invertible Elements and Topological Spectrum},
url = {http://eudml.org/doc/280628},
volume = {54},
year = {2006},
}

TY - JOUR
AU - Mati Abel
AU - Wiesław Żelazko
TI - Topologically Invertible Elements and Topological Spectrum
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2006
VL - 54
IS - 3
SP - 257
EP - 271
AB - Properties of topologically invertible elements and the topological spectrum of elements in unital semitopological algebras are studied. It is shown that the inversion $x ↦ x^{-1}$ is continuous in every invertive Fréchet algebra, and singly generated unital semitopological algebras have continuous characters if and only if the topological spectrum of the generator is non-empty. Several open problems are presented.
LA - eng
KW - topologically invertible elements; topological spectrum; spectral mapping property; discontinuity of inversion; functional topological spectrum
UR - http://eudml.org/doc/280628
ER -