Partitions of the Spectrum of a Topological Algebra through Geometric hulls
Perturbation and spectral discontinuity in Banach algebras
We extend an example of B. Aupetit, which illustrates spectral discontinuity for operators on an infinite-dimensional separable Hilbert space, to a general spectral discontinuity result in abstract Banach algebras. This can then be used to show that given any Banach algebra, Y, one may adjoin to Y a non-commutative inessential ideal, I, so that in the resulting algebra, A, the following holds: To each x ∈ Y whose spectrum separates the plane there corresponds a perturbation of x, of the form z =...
Perturbation theorems for Hermitian elements in Banach algebras
Two well-known theorems for Hermitian elements in C*-algebras are extended to Banach algebras. The first concerns the solution of the equation ax - xb = y, and the second gives sharp bounds for the distance between spectra of a and b when a, b are Hermitian.
Picard's theorem, Mittag-Leffler methods, and continuity of characters on Fréchet algebras
Pontryagin duality and topological algebras
Power factorization in Banach algebras with a bounded approximate identity
Power series in locally convex algebras
Power-dominated elements in a Banach algebra
Prehermitian Elements and B*-Algebras.
Projective limits of topological algebras
Properties of the spectral radius in Banach algebras
Propriétés multiplicatives universelles de certains quotients d'algèbres de Fréchet
Pseudo-Banach algebras
Pseudo-inverses, holomorphic functions and Atkinson theory in Banach algebras.