Let 𝓐 be a compatible collection of bounded subsets in a normed linear space. We give a characterization of the following generalized Mazur intersection property: every closed convex set A ∈ 𝓐 is an intersection of balls.
Si calcolano alcuni spazi di interpolazione fra spazi di funzioni hölderiane.
Si caratterizzano alcuni spazi di interpolazione tra spazi di funzioni continue e domini di operatori ellittici del 2° ordine.
A Banach algebra A is called strict if the product morphism is continuous with respect to the weak norm in A ⊗ A. The following result is proved: A C*-algebra is strict if and only if all its irreducible representations are finite-dimensional and their dimensions are bounded.
We study strongly exposed points in general Köthe-Bochner Banach spaces X(E). We first give a characterization of strongly exposed points of the set of X-selections of a measurable multifunction Γ. We then apply this result to the study of strongly exposed points of the closed unit ball of X(E). Precisely we show that if an element f is a strongly exposed point of , then |f| is a strongly exposed point of and f(ω)/∥ f(ω)∥ is a strongly exposed point of for μ-almost all ω ∈ S(f).
Let be an analytic functional and let be the corresponding convolution operator on Sato’s space of hyperfunctions. We show that is surjective iff admits an elementary solution in iff the Fourier transform μ̂ satisfies Kawai’s slowly decreasing condition (S). We also show that there are such that is not surjective on .
Let A(Ω) denote the real analytic functions defined on an open set Ω ⊂ ℝⁿ. We show that a partial differential operator P(D) with constant coefficients is surjective on A(Ω) if and only if for any relatively compact open ω ⊂ Ω, P(D) admits (shifted) hyperfunction elementary solutions on Ω which are real analytic on ω (and if the equation P(D)f = g, g ∈ A(Ω), may be solved on ω). The latter condition is redundant if the elementary solutions are defined on conv(Ω). This extends and improves previous...
Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space of (ω)-quasianalytic functions of Beurling type of one variable, which admit a continuous linear right inverse. Also, we characterize those (ω)-ultradifferential operators which admit a continuous linear right inverse on for each compact interval [a,b] and we show that this property is in fact weaker than the existence of a continuous linear right inverse on .
Solving a problem of L. Schwartz, those constant coefficient partial differential operators are characterized that admit a continuous linear right inverse on or , an open set in . For bounded with -boundary these properties are equivalent to being very hyperbolic. For they are equivalent to a Phragmen-Lindelöf condition holding on the zero variety of the polynomial .