Automatic continuity in algebras of differentiable functions.
Banach algebras with unique uniform norm II
Semisimple commutative Banach algebras 𝓐 admitting exactly one uniform norm (not necessarily complete) are investigated. 𝓐 has this Unique Uniform Norm Property iff the completion U(𝓐) of 𝓐 in the spectral radius r(·) has UUNP and, for any non-zero spectral synthesis ideal ℐ of U(𝓐), ℐ ∩ 𝓐 is non-zero. 𝓐 is regular iff U(𝓐) is regular and, for any spectral synthesis ideal ℐ of 𝓐, 𝓐/ℐ has UUNP iff U(𝓐) is regular and for any spectral synthesis ideal ℐ of U(𝓐), ℐ = k(h(𝓐 ∩ ℐ)) (hulls...
Banach space properties of strongly tight uniform algebras
We use the work of J. Bourgain to show that some uniform algebras of analytic functions have certain Banach space properties. If X is a Banach space, we say X is strongif X and X* have the Dunford-Pettis property, X has the Pełczyński property, and X* is weakly sequentially complete. Bourgain has shown that the ball-algebras and the polydisk-algebras are strong Banach spaces. Using Bourgain’s methods, Cima and Timoney have shown that if K is a compact planar set and A is R(K) or A(K), then A and...
Beurling-Figà-Talamanca-Herz algebras
For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras . For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We prove that...
Boundaries of weak peak points in noncommutative algebras of Lipschitz functions
It has been shown that any Banach algebra satisfying ‖f 2‖ = ‖f‖2 has a representation as an algebra of quaternion-valued continuous functions. Whereas some of the classical theory of algebras of continuous complex-valued functions extends immediately to algebras of quaternion-valued functions, similar work has not been done to analyze how the theory of algebras of complex-valued Lipschitz functions extends to algebras of quaternion-valued Lipschitz functions. Denote by Lip(X, ) the algebra over...
Bourgain algebras of G-disc algebras
Calcul fonctionnel holomorphe dans les algèbres de Banach ultramétriques
Central decompositions for compact convex sets
Characterizations of amenable representations of compact groups
Let G be a locally compact group and let π be a unitary representation. We study amenability and H-amenability of π in terms of the weak closure of (π ⊗ π)(G) and factorization properties of associated coefficient subspaces (or subalgebras) in B(G). By applying these results, we obtain some new characterizations of amenable groups.
Cohomology theory on non commutative algebras of continuous functions
Compact failure of multiplicativity for linear maps between Banach algebras.
Complemented subalgebras of the Baire-1 functions defined on the interval .
Comportement local des fonctions continues sur un compact régulier d'un corps local
Concerning the Banach-Stone theorem
Continuité des caractères des algèbres localement multiplicativement convexes
Continuity of derivations from radical convolution algebras
Continuity versus boundedness of the spectral factorization mapping
This paper characterizes the Banach algebras of continuous functions on which the spectral factorization mapping 𝔖 is continuous or bounded. It is shown that 𝔖 is continuous if and only if the Riesz projection is bounded on the algebra, and that 𝔖 is bounded only if the algebra is isomorphic to the algebra of continuous functions. Consequently, 𝔖 can never be both continuous and bounded, on any algebra under consideration.
Decompositions of operator-valued representations of function algebras
Description of quotient algebras in function algebras containing continuous unbounded functions
Let X be a completely regular Hausdorff space, a cover of X, and the algebra of all -valued continuous functions on X which are bounded on every . A description of quotient algebras of is given with respect to the topologies of uniform and strict convergence on the elements of .
Deterministic homogenization of parabolic monotone operators with time dependent coefficients.