Square roots and quasi-square roots in locally multiplicatively convex algebras
Square roots of elements with an unbounded spectrum
Stability of a 2-dimensional functional equation in a class of vector variable functions.
Stability of commuting maps and Lie maps
Let A be an ultraprime Banach algebra. We prove that each approximately commuting continuous linear (or quadratic) map on A is near an actual commuting continuous linear (resp. quadratic) map on A. Furthermore, we use this analysis to study how close are approximate Lie isomorphisms and approximate Lie derivations to actual Lie isomorphisms and Lie derivations, respectively.
Stability of multipliers on Banach algebras.
Stable inverse-limit sequences and automatic continuity
The elementary theory of stable inverse-limit sequences, introduced in stable inverse-limit sequences, is used to extend the 'stability lemma' of automatic continuity theory.
Stable inverse-limit sequences, with application to Predict algebras
The notion of a stable inverse-limit sequence is introduced. It provides a sufficient (and, for sequences of abelian groups, necessary) condition for the preservation of exactness by the inverse-limit functor. Examples of stable sequences are provided through the abstract Mittag-Leffler theorem; the results are applied in the theory of Fréchet algebras.
Stably flat completions of universal enveloping algebras [Book]
Statistical independence of operator algebras
Strict topologies as topological algebras
Let be a completely regular Hausdorff space, the space of all scalar-valued bounded continuous functions on with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally -convex.
Strongly compact algebras.
An algebra of bounded linear operators on a Hilbert space is said to be strongly compact if its unit ball is relatively compact in the strong operator topology. A bounded linear operator on a Hilbert space is said to be strongly compact if the algebra generated by the operator and the identity is strongly compact. This notion was introduced by Lomonosov as an approach to the invariant subspace problem for essentially normal operators. First of all, some basic properties of strongly compact algebras...
Structure -convexe d’une algèbre limite inductive localement convexe d’algèbres de Banach
Structure of locally idempotent algebras.
Structure theory of homologically trivial and annihilator locally C*-algebras
We study the structure of certain classes of homologically trivial locally C*-algebras. These include algebras with projective irreducible Hermitian A-modules, biprojective algebras, and superbiprojective algebras. We prove that, if A is a locally C*-algebra, then all irreducible Hermitian A-modules are projective if and only if A is a direct topological sum of elementary C*-algebras. This is also equivalent to A being an annihilator (dual, complemented, left quasi-complemented, or topologically...
Subsets of nonempty joint spectrum in topological algebras
We give a necessary and a sufficient condition for a subset of a locally convex Waelbroeck algebra to have a non-void left joint spectrum In particular, for a Lie subalgebra we have if and only if generates in a proper left ideal. We also obtain a version of the spectral mapping formula for a modified left joint spectrum. Analogous theorems for the right joint spectrum and the Harte spectrum are also valid.
Sul teorema di Gelfand-Mazur
In this note we produce a complex algebra without characters and which does not contain a proper extension of the complex number field.
Sums of idempotents and a lemma of N. J. Kalton
A lemma of Gelfand-Hille type is proved. It is used to give an improved version of a result of Kalton on sums of idempotents.
Supersets for the spectrum of elements in extended Banach algebras.
Superstability for generalized module left derivations and generalized module derivations on a Banach module. II.
Superstability for generalized module left derivations and generalized module derivations on a Banach module. I.