A-realcompact spaces.
Relations between homomorphisms on a real function algebra and different properties (such as being inverse-closed and closed under bounded inversion) are studied.
Arens algebras, associated with commutative von Neumann algebras
Arens regularity and local reflexivity principle for Banach algebras.
Arens Regularity of K (X).
Arens regularity of module actions
We study the Arens regularity of module actions of Banach left or right modules over Banach algebras. We prove that if has a brai (blai), then the right (left) module action of on * is Arens regular if and only if is reflexive. We find that Arens regularity is implied by the factorization of * or ** when is a left or a right ideal in **. The Arens regularity and strong irregularity of are related to those of the module actions of on the nth dual of . Banach algebras for which Z( **) = but are...
Arens Semi-Regular Banach Algebras.
Arens-regularity of algebras arising from tensor norms.
Arithmetic aspect of operator algebras
Aronszajn orderings.
Aronszajn-Kolmogorov type theorems for positive definite kernels in locally convex spaces
Aronszajn-Smith conditions for open sets. (Conditions d'Aronszajn-Smith pour les ouverts de classe .)
Around Widder’s characterization of the Laplace transform of an element of
Let ϰ be a positive, continuous, submultiplicative function on such that for some ω ∈ ℝ, α ∈ and . For every λ ∈ (ω,∞) let for . Let be the space of functions Lebesgue integrable on with weight , and let E be a Banach space. Consider the map . Theorem 5.1 of the present paper characterizes the range of the linear map defined on , generalizing a result established by B. Hennig and F. Neubrander for . If ϰ ≡ 1 and E =ℝ then Theorem 5.1 reduces to D. V. Widder’s characterization...
Arrival time observables in quantum mechanics
Arzela - Ascoli's Theorem for Riemann - Integrable Functions on Compact Spaces.
Ascent and descent of weighted composition operators on L^p-spaces
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.
Aspects of unconditionality of bases in spaces of compact operators
E. Tutaj has introduced classes of Schauder bases termed "unconditional-like" (UL) and "unconditional-like*" (UL*) whose intersection is the class of unconditional bases. In view of this association with unconditional bases, it is interesting to note that there exist Banach spaces which have no unconditional basis and yet have a basis of one of these two types (e.g., the space 𝓞[0,1]). In the same spirit, we show in this paper that the space of all compact operators on a reflexive Banach space...
Asplund Functions and Projectional Resolutions of the Identity
*Supported by the Grants AV ˇCR 101-97-02, 101-90-03, GA ˇCR 201-98-1449, and by the Grant of the Faculty of Civil Engineering of the Czech Technical University No. 2003.We further develop the theory of the so called Asplund functions, recently introduced and studied by W. K. Tang. Let f be an Asplund function on a Banach space X. We prove that (i) the subspace Y := sp ∂f(X) has a projectional resolution of the identity, and that (ii) if X is weakly Lindel¨of determined, then X admits a projectional...
Asplund operators and holomorphic maps.
Asplund spaces