A characterization of the -realcompact space
A multiplicative functional on the commutative topological field
A note on commutative Banach algebras.
Algebras of Special Singular Integrals over Local Fields.
Aspects of the theory of derivations
We survey some old and new results in the theory of derivations on Banach algebras. Although our overview is broad ranging, our principal interest is in recent results concerning conditions on a derivation implying that its range is contained in the radical of the algebra.
Banach algebra techniques in the theory of arithmetic functions
For infinite discrete additive semigroups we study normed algebras of arithmetic functions endowed with the linear operations and the convolution. In particular, we investigate the problem of scaling the mean deviation of related multiplicative functions for . This involves an extension of Banach algebras of arithmetic functions by introducing weight functions and proving a weighted inversion theorem of Wiener type in the frame of Gelfand’s theory of commutative Banach algebras.
Continuous derivations of valued fields
Convolution on the reduced dual of a locally compact group.
Forme algébrique des théories de Stone-Gel'fand
Generalized group algebras and their bundles.
Homomorphismes d'espaces de Banach de fonctions continues
Invertible elements in a convolution algebra of holomorphic functions.
Newton interpolating series at distinct points with coefficients in a real Banach algebra.
On differential subspaces of Cartesian space
Operator-valued analytic functions of constant norm
Product integral in a Fréchet algebra.
Produit tensoriel topologique des corps values.
Properties of derivations on some convolution algebras
For all convolution algebras L 1[0, 1); L loc1 and A(ω) = ∩n L 1(ωn), the derivations are of the form D μ f = Xf * μ for suitable measures μ, where (Xf)(t) = tf(t). We describe the (weakly) compact as well as the (weakly) Montel derivations on these algebras in terms of properties of the measure μ. Moreover, for all these algebras we show that the extension of D μ to a natural dual space is weak-star continuous.
Pure quasi-states and extremal quasi-measures.
Rational modules and higher order Cauchy transforms.