2-normed Algebras-I
A -algebra without generalized topological divisors of zero
A -algebra on Schur algebras.
A characterization of commutativity for non-associative normed algebras.
A characterization of homomorphisms in certain Banach involution algebras
A characterization of maximal regular ideals in lmc algebras
A question of Warner and Whitley concerning a nonunital version of the Gleason-Kahane-Żelazko theorem is considered in the context of nonnormed topological algebras. Among other things it is shown that a closed hyperplane M of a commutative symmetric F*-algebra E with Lindelöf Gel'fand space is a maximal regular ideal iff each element of M belongs to some closed maximal regular ideal of E.
A characterization of multiplicative linear functionals in Banach algebras
A characterization of Q-algebras of type F
We prove that a real or complex unital F-algebra is a Q-algebra if and only if all its maximal one-sided ideals are closed.
A characterization of singular endomorphisms of a barrelled Ptak space.
A continuous semicharacter
A criterion for subharmonicity of a function of the spectrum
A generalization of Gelfand-Mazur theorem.
A geometric condition equivalent to commutativity in Banach algebras
A Jacobson-semisimple Banach algebra with a dense nil subalgebra
A Kleinecke-Shirokov type condition with Jordan automorphisms
Let φ be a Jordan automorphism of an algebra . The situation when an element a ∈ satisfies is considered. The result which we obtain implies the Kleinecke-Shirokov theorem and Jacobson’s lemma.
A measure induced metric topology for a Banach algebra
A non-Banach in-convex algebra all of whose closed commutative subalgebras are Banach algebras.
We construct two examples of complete multiplicatively convex algebras with the property that all their maximal commutative subalgebras and consequently all commutative closed subalgebras are Banach algebras. One of them is non-metrizable and the other is metrizable and non-Banach. This solves Problems 12-16 and 22-24 of [7].
A non-locally convex topological algebra with all commutative subalgebras locally convex
We construct a complete multiplicatively pseudoconvex algebra with the property announced in the title. This solves Problem 25 of [6].
A non-m-convex algebra on which operate all entire functions
A note on criteria of Le Page and Hirschfeld-Żelazko for the commutativity of Banach algebras