Two-norm spaces and decompositions of Banach spaces, I
Type and cotype of operator spaces
We consider two operator space versions of type and cotype, namely -type, -cotype and type (p,H), cotype (q,H) for a homogeneous Hilbertian operator space H and 1 ≤ p ≤ 2 ≤ q ≤ ∞, generalizing “OH-cotype 2” of G. Pisier. We compute type and cotype of some Hilbertian operator spaces and spaces, and we investigate the relationship between a homogeneous Hilbertian space H and operator spaces with cotype (2,H). As applications we consider operator space versions of generalized little Grothendieck’s...
Type and cotype of some Banach spaces.
Type, cotype et mesures de Levy sur les espaces de Banach
«Type» des espaces normés
Type et cotype dans les espaces munis de structures locales inconditionnelles
Type, infratype and the Elton-Pajor theorem.
Types of tightness in spaces with unconditional basis
We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal's list related to Gowers' classification program of Banach spaces, but in contrast to the recently constructed space of type (4), our space is also tight with constants, thus essentially extending the list of known examples in Gowers' program. The space is defined on the basis of a boundedly modified mixed Tsirelson space with the use of a special coding...
Types on stable Banach spaces
We prove a geometric characterization of Banach space stability. We show that a Banach space X is stable if and only if the following condition holds. Whenever is an ultrapower of X and B is a ball in , the intersection B ∩ X can be uniformly approximated by finite unions and intersections of balls in X; furthermore, the radius of these balls can be taken arbitrarily close to the radius of B, and the norm of their centers arbitrarily close to the norm of the center of B. The preceding condition...
Typical sets and typical continuous functions
Über analytische Fortsetzung in Banachräumen.
Über das Spektrum positiver Generatoren.
Über den Zusammenhang von schlichten Funktionen im Banachraum B.
Über die Cunningham-oo-Algebra und den Zentralisator reeller Banachräume.
Über Differentialgleichungen in n. a. Banachräumen, insbesondere ihre Lösung mittels eines ,, Wegintegrales".
Über eine Klasse symmetrischer idealer Funktionenräume nebst Anwendungen
Über homöomorphe und differenzierbare Abbildungen N.A. Banachräume.
Über Sobolevsche Räume mit Belegungsfunktion und das Dirichletsche Problem (Vorläufige Mitteilung)
Über symmetrische Operatoren auf Banachverbänden und Arens-Regularität
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.