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We consider the topological algebra of (Taylor) multipliers on spaces of real analytic functions of one variable, i.e., maps for which monomials are eigenvectors. We describe multiplicative functionals and algebra homomorphisms on that algebra as well as idempotents in it. We show that it is never a Q-algebra and never locally m-convex. In particular, we show that Taylor multiplier sequences cease to be so after most permutations.
Nella prima parte della nota sono studiate le proprietà di connessione dei sottospazi dello spettro di un anello. Con l’ausilio dei risultati ottenuti, si stabiliscono le condizioni necessarie e sufficienti affinchè un’algebra reale assolutamente piatta sia isomorfa ad un’algebra di funzioni continue a valori reali su un -spazio, del quale determini la topologia. Ulteriori condizioni sono necessarie e sufficienti affinché un’algebra reale assolutamente piatta sia isomorfa all’algebra di tutte le...
We prove that there exists an example of a metrizable non-discrete space , such that but where and is the space of all continuous functions from into reals equipped with the topology of pointwise convergence. It answers a question of Arhangel’skii ([2, Problem 4]).
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