An example is given of a semisimple commutative Banach algebra that has the strong spectral extension property but fails the multiplicative Hahn-Banach property. This answers a question posed by M. J. Meyer in [4].
In this report we discuss the applications of the strong unicity constant and highlight its use in the minimal projection problem.
Let X be a real or complex vector space equipped with the strongest vector space topology . Besides the result announced in the title we prove that X is uncountable-dimensional if and only if it is not locally pseudoconvex.
Lindenstrauss-Pełczyński (for short ℒ) spaces were introduced by these authors [Studia Math. 174 (2006)] as those Banach spaces X such that every operator from a subspace of c₀ into X can be extended to the whole c₀. Here we obtain the following structure theorem: a separable Banach space X is an ℒ-space if and only if every subspace of c₀ is placed in X in a unique position, up to automorphisms of X. This, in combination with a result of Kalton [New York J. Math. 13 (2007)], provides a negative...
Sea X un espacio de Banach con una base incondicional de Schauder no numerable, y sea Y un subespacio arbitrario no separable de X. Si X no contiene una copia isomorfa de l1(J) con J no numerable entonces (1) la densidad de Y y la débil*-densidad de Y* son iguales, y (2) la bola unidad de X* es débil* sucesionalmente compacta. Además, (1) implica que Y contiene subconjuntos grandes formados por elementos disjuntos dos a dos, y una propiedad similar se verifica para las bases incondicionales no numerables...