@misc{10481/33543,
year = {2014},
url = {http://hdl.handle.net/10481/33543},
abstract = {We define the spectrum of an element a in a non-associative algebra A according to a classical notion of invertibility (a is invertible if the multiplication operators La and Ra are bijective). Around this notion of spectrum, we develop a basic theoretical support for a non-associative spectral theory. Thus we prove some classical theorems of automatic continuity free of the requirement of associativity. In particular, we show the uniqueness of the complete norm topology of m-semisimple algebras, obtaining as a corollary of this result a well-known theorem of Barry E. Johnson (1967). The celebrated result of C.E. Rickart (1960) about the continuity of dense-range homomorphisms is also studied in the non-associative framework. Finally, because non-associative algebras are very suitable models in genetics, we provide here a hint of how to apply this approach in that context, by showing that every homomorphism from a complete normed algebra onto a particular type of evolution algebra is automatically continuous.},
organization = {Research supported by Junta de Andaluc´ıa grant FQM 0199.},
publisher = {Univerzitet U Nišu},
keywords = {Spectrum},
keywords = {Spectral radius},
keywords = {Non-associative complete normed algebra},
keywords = {Radical},
keywords = {Homomorphism},
keywords = {Continuity},
keywords = {Genetic algebra},
title = {The multiplicative spectrum and the uniqueness of the complete norm topology},
doi = {10.2298/FIL1403473M},
author = {Marcos Sánchez, Juan Carlos and Velasco Collado, María Victoria},
}