Über die Ecken des numerischen Wertebereches in einer Banachalgebra.
Über die Ecken des numerischen Wertebereiches in einer Banachalgebra. II.
Über die Klassifikation der symmetrischen hermiteschen Mannigfaltigkeiten unendlicher Dimension. I.
U-ideals of factorable operators
We suggest a method of renorming of spaces of operators which are suitably approximable by sequences of operators from a given class. Further we generalize J. Johnsons’s construction of ideals of compact operators in the space of bounded operators and observe e.g. that under our renormings compact operators are -ideals in the: space of 2-absolutely summing operators or in the space of operators factorable through a Hilbert space.
Ultraproducts in Banach space theory.
Uncomplementability of spaces of compact operators in larger spaces of operators
In the first part of the paper we prove some new result improving all those already known about the equivalence of the nonexistence of a projection (of any norm) onto the space of compact operators and the containment of in the same space of compact operators. Then we show several results implying that the space of compact operators is uncomplemented by norm one projections in larger spaces of operators. The paper ends with a list of questions naturally rising from old results and the results...
Unconditional decompositions and local unconditional structures in some subspaces of , 1≤p<2
Unconditionally converging operators in locally convex Hausdorff spaces
Une classe d'ensembles analytiques à plusieurs dimensions
Uniformly continuous functionals on Banach algebras
Uniqueness of complete norms for quotients of Banach function algebras
We prove that every quotient algebra of a unital Banach function algebra A has a unique complete norm if A is a Ditkin algebra. The theorem applies, for example, to the algebra A (Γ) of Fourier transforms of the group algebra of a locally compact abelian group (with identity adjoined if Γ is not compact). In such algebras non-semisimple quotients arise from closed subsets E of Γ which are sets of non-synthesis. Examples are given to show that the condition of Ditkin cannot be relaxed. We construct...
Uniqueness of rotation invariant norms.
Uniqueness of the topology on L¹(G)
Let G be a locally compact abelian group and let X be a translation invariant linear subspace of L¹(G). If G is noncompact, then there is at most one Banach space topology on X that makes translations on X continuous. In fact, the Banach space topology on X is determined just by a single nontrivial translation in the case where the dual group Ĝ is connected. For G compact we show that the problem of determining a Banach space topology on X by considering translation operators on X is closely related...
Unital strongly harmonic commutative Banach algebras
A unital commutative Banach algebra is spectrally separable if for any two distinct non-zero multiplicative linear functionals φ and ψ on it there exist a and b in such that ab = 0 and φ(a)ψ(b) ≠ 0. Spectrally separable algebras are a special subclass of strongly harmonic algebras. We prove that a unital commutative Banach algebra is spectrally separable if there are enough elements in such that the corresponding multiplication operators on have the decomposition property (δ). On the other hand,...
Unitary Banach algebras
In a Banach algebra an invertible element which has norm one and whose inverse has norm one is called unitary. The algebra is unitary if the closed convex hull of the unitary elements is the closed unit ball. The main examples are the C*-algebras and the ℓ₁ group algebra of a group. In this paper, different characterizations of unitary algebras are obtained in terms of numerical ranges, dentability and holomorphy. In the process some new characterizations of C*-algebras are given.
Unité Et Semi-Normes Dans Les Algèbres Localement Convexes.
Universal estimates of the spectral radius