Multiplicative functionals and entire functions
Let A be a complex Banach algebra with a unit e, let T, φ be continuous functionals, where T is linear, and let F be a nonlinear entire function. If T ∘ F = F ∘ φ and T(e) = 1 then T is multiplicative.
Multiplicative functionals and entire functions, II
Let A be a complex Banach algebra with a unit e, let F be a nonconstant entire function, and let T be a linear functional with T(e)=1 and such that T∘F: A → ℂ is nonsurjective. Then T is multiplicative.
Multiplier algebras, Banach bundles, and one-parameter semigroups
Multipliers of Imprimitivity Bimodules and Morita Equivalence of Crossed Products.
Multipliers of JS-Algebras.
Multipliers of Segal algebras.
Multipliers of topological algebras [Book]
Multipliers on Banach algebras
Multipliers, self-induced and dual Banach algebras [Book]
Multi-valued superpositions [Book]
Mutations of C*-algebras and quasiassociative JB*-algebras
New associative and nonassociative Gelfand-Naimark theorems.
Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra
Generalizing earlier results about the set of idempotents in a Banach algebra, or of self-adjoint idempotents in a -algebra, we announce constructions of nice connecting paths in the connected components of the set of elements in a Banach algebra, or of self-adjoint elements in a -algebra, that satisfy a given polynomial equation, without multiple roots. In particular, we prove that in the Banach algebra case every such non-central element lies on a complex line, all of whose points satisfy the...
Nil, nilpotent and PI-algebras
The notions of nil, nilpotent or PI-rings (= rings satisfying a polynomial identity) play an important role in ring theory (see e.g. [8], [11], [20]). Banach algebras with these properties have been studied considerably less and the existing results are scattered in the literature. The only exception is the work of Krupnik [13], where the Gelfand theory of Banach PI-algebras is presented. However, even this work has not get so much attention as it deserves. The present paper...
Nilpotent elements and solvable actions.
In what follows we shall describe, in terms of some commutation properties, a method which gives nilpotent elements. Using this method we shall describe the irreducibility for Lie algebras which have Levi-Malçev decomposition property.
Nilpotente Liesche Gruppen haben symmetrische Gruppenalgebren.
Noetherian Banach Algebras are Finite Dimensional.
(Non-)amenability of ℬ(E)
In 1972, the late B. E. Johnson introduced the notion of an amenable Banach algebra and asked whether the Banach algebra ℬ(E) of all bounded linear operators on a Banach space E could ever be amenable if dim E = ∞. Somewhat surprisingly, this question was answered positively only very recently as a by-product of the Argyros-Haydon result that solves the “scalar plus compact problem”: there is an infinite-dimensional Banach space E, the dual of which is ℓ¹, such that . Still, ℬ(ℓ²) is not amenable,...
Nonassociative normed algebras: geometric aspects
Introduction. The aim of this paper is to review some relevant results concerning the geometry of nonassociative normed algebras, without assuming in the first instance that such algebras satisfy any familiar identity, like associativity, commutativity, or Jordan axiom. In the opinion of the author, the most impressive fact in this direction is that most of the celebrated natural geometric conditions that can be required for associative normed algebras, when imposed on a general nonassociative...
Nonassociative real H*-algebras.
We prove that, if A denotes a topologically simple real (non-associative) H*-algebra, then either A is a topologically simple complex H*-algebra regarded as real H*-algebra or there is a topologically simple complex H*-algebra B with *-involution τ such that A = {b ∈ B : τ(b) = b*}. Using this, we obtain our main result, namely: (algebraically) isomorphic topologically simple real H*-algebras are actually *-isometrically isomorphic.