-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation.
-absolutely summing operators on the space and applications.
(-)orthogonality in -adic Banach spaces
-Spaces and cone summing operators
1-amenability of 𝒜(X) for Banach spaces with 1-unconditional bases
The main result of the note is a characterization of 1-amenability of Banach algebras of approximable operators for a class of Banach spaces with 1-unconditional bases in terms of a new basis property. It is also shown that amenability and symmetric amenability are equivalent concepts for Banach algebras of approximable operators, and that a type of Banach space that was long suspected to lack property 𝔸 has in fact the property. Some further ideas on the problem of whether or not amenability (in...
2-summing multiplication operators
Let 1 ≤ p < ∞, be a sequence of Banach spaces and the coresponding vector valued sequence space. Let , be two sequences of Banach spaces, , Vₙ: Xₙ → Yₙ, a sequence of bounded linear operators and 1 ≤ p,q < ∞. We define the multiplication operator by . We give necessary and sufficient conditions for to be 2-summing when (p,q) is one of the couples (1,2), (2,1), (2,2), (1,1), (p,1), (p,2), (2,p), (1,p), (p,q); in the last case 1 < p < 2, 1 < q < ∞.
A Banach space determined by the Weil height
A Banach space dichotomy theorem for quotients of subspaces
A Banach space X with a Schauder basis is defined to have the restricted quotient hereditarily indecomposable property if X/Y is hereditarily indecomposable for any infinite-codimensional subspace Y with a successive finite-dimensional decomposition on the basis of X. The following dichotomy theorem is proved: any infinite-dimensional Banach space contains a quotient of a subspace which either has an unconditional basis, or has the restricted quotient hereditarily indecomposable property.
A Banach space that is MLUR but not HR.
A Banach space with a symmetric basis which contains no or , and all its symmetric basic sequences are equivalent
A Banach space with a symmetric basis which is of weak cotype 2 but not of cotype 2
We prove that the symmetric convexified Tsirelson space is of weak cotype 2 but not of cotype 2.
A Bator's question on dual Banach spaces.
A bilinear version of Holsztyński's theorem on isometries of C(X)-spaces
We prove that, for a compact metric space X not reduced to a point, the existence of a bilinear mapping ⋄: C(X) × C(X) → C(X) satisfying ||f⋄g|| = ||f|| ||g|| for all f,g ∈ C(X) is equivalent to the uncountability of X. This is derived from a bilinear version of Holsztyński's theorem [3] on isometries of C(X)-spaces, which is also proved in the paper.
A bornological approach to rotundity and smoothness applied to approximation.
A certain subspace of characteristic zero of
A Characteriaztion of Conjugate WCG Banach Spaces.
A characterization of -convexity and -convexity of Banach spaces.
A characterization of complex -preduals via a complex barycentric mapping
We provide a complex version of a theorem due to Bednar and Lacey characterizing real -preduals. Hence we prove a characterization of complex -preduals via a complex barycentric mapping.
A Characterization of M-Bases.
A characterization of reflexivity in terms of the existence of generalized centers.