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Continuity of homomorphisms into power-associative complete normed algebras
-
J. Carlos Marcos
and
M. Victoria Velasco
Published/Copyright:
January 10, 2011
Abstract.
Let A and B be complete normed algebras with a unit such that B is
simple and power-associative, and let 
be a
dense-range homomorphism. We prove that if θ is irreducible (that
is, 
, for every closed proper ideal I of A), then θ is continuous. The continuity of non-irreducible homomorphisms is
also obtained provided that the set of «spectrally rare
»elements in the range algebra is not dense in B. These
results extend the classical Rickart's dense-range homomorphism theorem to
the non-associative setting.
Received: 2011-08-04
Revised: 2011-11-03
Published Online: 2011-01-10
Published in Print: 2013-11-01
© 2013 by Walter de Gruyter Berlin Boston
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- Continuity of homomorphisms into power-associative complete normed algebras
- The connection problem associated with a Selberg type integral and the q-Racah polynomials
- The space of linear maps into a Grassmann manifold
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Keywords for this article
Continuity;
homomorphism;
non-associative;
normed algebra;
spectrum;
power-associative
Articles in the same Issue
- Masthead
- Continuity of homomorphisms into power-associative complete normed algebras
- The connection problem associated with a Selberg type integral and the q-Racah polynomials
- The space of linear maps into a Grassmann manifold
- The integral cohomology of configuration spaces of pairs of points in real projective spaces
- The tree of irreducible numerical semigroups with fixed Frobenius number
- The topological decomposition of inverse limits of iterated wreath products of finite Abelian groups
- Comparison principles and Dirichlet problem for fully nonlinear degenerate equations of Monge–Ampère type
