An abstract version of Herz' imbedding theorem
An additivity formula for the strict global dimension of C(Ω)
Let A be a unital strict Banach algebra, and let K + be the one-point compactification of a discrete topological space K. Denote by the weak tensor product of the algebra A and C(K +), the algebra of continuous functions on K +. We prove that if K has sufficiently large cardinality (depending on A), then the strict global dimension is equal to .
An algebra associated with the generalized sublaplacian
An algebraic characterization of complete inner product spaces.
An algebraic characterization of quasi-Möbius homeomorphisms. (Une caractérisation algébrique des homéomorphismes quasi-Möbius.)
An algebraic formulation of ergodic problems
An algebraic view of distributions and operators
An algevraic study of the Kolmogorov entropy
An almost nowhere Fréchet smooth norm on superreflexive spaces
Every separable infinite-dimensional superreflexive Banach space admits an equivalent norm which is Fréchet differentiable only on an Aronszajn null set.
An Almost Orthogonal Radial Wavelet Expansion for Radial Distributions.
An alternative Dunford-Pettis Property
An alternative to the Dunford-Pettis Property, called the DP1-property, is introduced. Its relationship to the Dunford-Pettis Property and other related properties is examined. It is shown that -direct sums of spaces with DP1 have DP1 if 1 ≤ p < ∞. It is also shown that for preduals of von Neumann algebras, DP1 is strictly weaker than the Dunford-Pettis Property, while for von Neumann algebras, the two properties are equivalent.
An alternative polynomial Daugavet property
We introduce a weaker version of the polynomial Daugavet property: a Banach space X has the alternative polynomial Daugavet property (APDP) if every weakly compact polynomial P: X → X satisfies . We study the stability of the APDP by c₀-, - and ℓ₁-sums of Banach spaces. As a consequence, we obtain examples of Banach spaces with the APDP, namely and C(K,X), where X has the APDP.
An alternative proof of Petty's theorem on equilateral sets
The main goal of this paper is to provide an alternative proof of the following theorem of Petty: in a normed space of dimension at least three, every 3-element equilateral set can be extended to a 4-element equilateral set. Our approach is based on the result of Kramer and Németh about inscribing a simplex into a convex body. To prove the theorem of Petty, we shall also establish that for any three points in a normed plane, forming an equilateral triangle of side p, there exists a fourth point,...
An amalgamation of the Banach spaces associated with James and Schreier, Part I: Banach-space structure
We create a new family of Banach spaces, the James-Schreier spaces, by amalgamating two important classical Banach spaces: James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. We then investigate the properties of these James-Schreier spaces, paying particular attention to how key properties of their 'ancestors' (that is, the James space and the Schreier space) are expressed in them. Our main results include...
An amalgamation of the Banach spaces associated with James and Schreier, Part II: Banach-algebra structure
The James-Schreier spaces, defined by amalgamating James' quasi-reflexive Banach spaces and Schreier space, can be equipped with a Banach-algebra structure. We answer some questions relating to their cohomology and ideal structure, and investigate the relations between them. In particular we show that the James-Schreier algebras are weakly amenable but not amenable, and relate these algebras to their multiplier algebras and biduals.
An analogue in commutative harmonic analysis of the uniform bounded approximation property of Banach space
An Analogue of a Hardy-Littlewood-Fejér Inequality for Upper Triangular Trace Class Operators.
An analogue of the Riesz-representation theorem.
An analytic approach to the spectral characterization of the radical
We give a simple complex-variable proof of an old result of Zemánek and Le Page on the radical of a Banach algebra. Incidentally, the argument also proves a recent result of Harris and Kadison.
An analytic solution to the Busemann-Petty problem on sections of convex bodies.