Factorization in some Fréchet algebras of differentiable functions
Finite dimensionality in socle of Banach algebras.
Finite rank elements in semisimple Banach algebras
Let A be a semisimple Banach algebra. We define the rank of a nonzero element a in the socle of A to be the minimum of the number of minimal left ideals whose sum contains a. Several characterizations of rank are proved.
Finite spectra and quasinilpotent equivalence in Banach algebras
This paper further investigates the implications of quasinilpotent equivalence for (pairs of) elements belonging to the socle of a semisimple Banach algebra. Specifically, not only does quasinilpotent equivalence of two socle elements imply spectral equality, but also the trace, determinant and spectral multiplicities of the elements must agree. It is hence shown that quasinilpotent equivalence is established by a weaker formula (than that of the spectral semidistance). More generally, in the second...
Finiteness properties of topological algebras, I
Fixed point characterization of left amenable Lau algebras.
Fonctions entières et théorèmes de Banach-Steinhaus dans certaines algèbres complètes
Fréchet algebras with orthogonal basis
Fredholm, Riesz and local spectral theory of multipliers.
Fredholm theory in Banach algebras
Functional continuity of commutative m-convex -algebras with countable maximal ideal spaces
Functionals on Banach Algebras with Scattered Spectra
Let A be a complex, commutative Banach algebra and let be the structure space of A. Assume that there exists a continuous homomorphism h:L¹(G) → A with dense range, where L¹(G) is a group algebra of the locally compact abelian group G. The main results of this note can be summarized as follows: (a) If every weakly almost periodic functional on A with compact spectra is almost periodic, then the space is scattered (i.e., has no nonempty perfect subset). (b) Weakly almost periodic functionals...
Funtional Boundedness of Some M-Complete m-Convex Algebras
Gateaux Differentials in Banach Algebras.
Generalization of the Shirali-Ford theorem in Hermitian locally multiplicatively convex algebras
Generalized almost periodic functions
Generalizing normality for operators on Banach spaces: Hyponormality. I.
Géométrie du spectre dans une algèbre de Banach et domaine numérique
Dans une algèbre de Banach et dans deux cas particuliers, nous montrons la continuité du centre du plus petit disque contenant le spectre. Pour a ∈ , on donne une condition nécessaire et suffisante pour avoir où d(a) est la distance de a aux scalaires et le rayon du plus petit disque contenant K qui représente le spectre ou le domaine numérique algébrique de a. Dans un espace de Hilbert complexe, K peut représenter certains types de spectres ou de domaines numériques de a.
Geometry of numerical ranges in locally -convex *-algebras.
Geometry of the spectral semidistance in Banach algebras
Let be a unital Banach algebra over , and suppose that the nonzero spectral values of and are discrete sets which cluster at , if anywhere. We develop a plane geometric formula for the spectral semidistance of and which depends on the two spectra, and the orthogonality relationships between the corresponding sets of Riesz projections associated with the nonzero spectral values. Extending a result of Brits and Raubenheimer, we further show that and are quasinilpotent equivalent if...