The group of invertible elements of a commutative Banach algebra
The inverse spectral radius formula and removability of spectrum
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 metric space , 0
The non-archimedean Corona problem
The non-archimedean space
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 projective limit of the spaces
The range of Toeplitz operators on the ball.
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 space of functions with a limit at each point.
The space of multipliers into
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 a class of Banach algebras generated by a Banach space
The structure of homomorphisms from Banach algebras of differentiable functions into finite dimensional Banach algebras.
The structure of ideals in the Banach algebra of Lipschitz functions over valued fields
The structure of L-ideals of measure algebras. II