Continuity of homomorphisms into complete normed algebraic algebras
نویسندگان
چکیده
We prove that, if A and B are complete normed non-associative algebras, and if B is strongly semisimple and algebraic, then dense range homomorphisms from A to B are continuous. As a consequence, we obtain that homomorphisms from complete normed algebras into a complete normed power-associative algebraic algebra B are continuous if and only if B has no nonzero elements with zero square. We also show that homomorphisms from complete normed algebras into a finite-dimensional algebra B are continuous if and only if B has no nonzero elements with zero square. 2003 Elsevier Science (USA). All rights reserved.
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