Tensor product of URM algbras
The compactum of a semi-simple commutative Banach algebra.
The generalized corona theorem.
The kh-socle of a commutative semisimple Banach algebra
Let be a commutative complex semisimple Banach algebra. Denote by the kernel of the hull of the socle of . In this work we give some new characterizations of this ideal in terms of minimal idempotents in . This allows us to show that a “result” from Riesz theory in commutative Banach algebras is not true.
The Maximal Ideal Space of a Banach Algebra of Multipliers.
The non-archimedean Corona problem
The norm of uniform convergence on the -algebraic maximal spectrum of an algebra over a non-archimedean valuation field
The norm spectrum in certain classes of commutative Banach algebras
Let A be a commutative Banach algebra and let be its structure space. The norm spectrum σ(f) of the functional f ∈ A* is defined by , where f·a is the functional on A defined by ⟨f·a,b⟩ = ⟨f,ab⟩, b ∈ A. We investigate basic properties of the norm spectrum in certain classes of commutative Banach algebras and present some applications.
The Pełczyński property for some uniform algebras
The Słodkowski spectra and higher Shilov boundaries
We investigate relations between the spectra defined by Słodkowski [14] and higher Shilov boundaries of the Taylor spectrum. The results generalize the well-known relation between the approximate point spectrum and the usual Shilov boundary.
The strong spectral extension property does not imply the multiplicative Hahn-Banach property
An example is given of a semisimple commutative Banach algebra that has the strong spectral extension property but fails the multiplicative Hahn-Banach property. This answers a question posed by M. J. Meyer in [4].
The structure of ideals in the Banach algebra of Lipschitz functions over valued fields
The structure of L-ideals of measure algebras. II
The structure of polynomial ideals in the algebra of entire functions
The Theorem of Gleason-Kahane-Zelazko in a Commutative Symmetric Banach Algebra.
Topología grassmaniana sobre los ideales cerrados de codimensión finita de un álgebra de Banach conmutativa.
Topologies on the Extreme Points of Compact Convex Sets II.
Topologies on the space of ideals of a Banach algebra
Some topologies on the space Id(A) of two-sided and closed ideals of a Banach algebra are introduced and investigated. One of the topologies, namely , coincides with the so-called strong topology if A is a C*-algebra. We prove that for a separable Banach algebra coincides with a weaker topology when restricted to the space Min-Primal(A) of minimal closed primal ideals and that Min-Primal(A) is a Polish space if is Hausdorff; this generalizes results from [1] and [5]. All subspaces of Id(A)...
Trivial generators for nontrivial fibres
Pseudoconvex domains are exhausted in such a way that we keep a part of the boundary fixed in all the domains of the exhaustion. This is used to solve a problem concerning whether the generators for the ideal of either the holomorphic functions continuous up to the boundary or the bounded holomorphic functions, vanishing at a point in where the fibre is nontrivial, has to exceed . This is shown not to be the case.