A new extension theorem for concave operators.
A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces [Book]
A new function space and applications
We define a new function space , which contains in particular BMO, BV, and , . We investigate its embedding into Lebesgue and Marcinkiewicz spaces. We present several inequalities involving norms of integer-valued functions in . We introduce a significant closed subspace, , of , containing in particular VMO and , . The above mentioned estimates imply in particular that integer-valued functions belonging to are necessarily constant. This framework provides a “common roof” to various,...
A New Hereditarily l^2 Banach Space
2000 Mathematics Subject Classification: 46B20, 46B26.We construct a non-reflexive, l^2 saturated Banach space such that every non-reflexive subspace has non-separable dual.
A New Isoperimetric Inequality for Product Measure and the Tails of Sums of Independent Variables.
A new look on Hankel forms over Fock space
A new metric invariant for Banach spaces
We show that if the Szlenk index of a Banach space X is larger than the first infinite ordinal ω or if the Szlenk index of its dual is larger than ω, then the tree of all finite sequences of integers equipped with the hyperbolic distance metrically embeds into X. We show that the converse is true when X is assumed to be reflexive. As an application, we exhibit new classes of Banach spaces that are stable under coarse-Lipschitz embeddings and therefore under uniform homeomorphisms.
A new of looking at distributional estimates; applications for the bilinear Hilbert transform.
Distributional estimates for the Carleson operator acting on characteristic functions of measurable sets of finite measure were obtained by Hunt. In this article we describe a simple method that yields such estimates for general operators acting on one or more functions. As an application we discuss how distributional estimates are obtained for the linear and bilinear Hilbert transform. These distributional estimates show that the square root of the bilinear Hilbert transform is exponentially lntegrable...
A new order relation for JB-algebras
A new proof for a Rolewicz's type theorem: An evolution semigroup approach.
A new proof for the multiplicative property of the boolean cumulants with applications to the operator-valued case
The paper presents several combinatorial properties of the boolean cumulants. A consequence is a new proof of the multiplicative property of the boolean cumulant series that can be easily adapted to the case of boolean independence with amalgamation over an algebra.
A new proof of a Lemma by Phelps.
A new proof of Fréchet differentiability of Lipschitz functions
We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on (or more generally on an Asplund space) has points of Fréchet differentiability. Somewhat more generally, we show that a real-valued Lipschitz function on a separable Banach space has points of Fréchet differentiability provided that the closure of the set of its points of Gâteaux differentiability is norm separable.
A new proof of James' sup theorem.
We provide a new proof of James' sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnson: "If a normed space E does not contain any asymptotically isometric copy of l1, then every bounded sequence of E' has a normalized l1-block sequence pointwise converging to 0".
A New Proof of Nakano's Theorem in Locally Solid Riesz Spaces.
A New Proof of the Fundamental Lemma of Interpolation Theory.
A new proof of the Jawerth-Franke embedding.
A new proof of the noncommutative Banach-Stone theorem
Surjective isometries between unital C*-algebras were classified in 1951 by Kadison [K]. In 1972 Paterson and Sinclair [PS] handled the nonunital case by assuming Kadison’s theorem and supplying some supplementary lemmas. Here we combine an observation of Paterson and Sinclair with variations on the methods of Yeadon [Y] and the author [S1], producing a fundamentally new proof of the structure of surjective isometries between (nonunital) C*-algebras. In the final section we indicate how our techniques...
A new relationship between decomposability and convexity
In the present work we prove that, in the space of Pettis integrable functions, any subset that is decomposable and closed with respect to the topology induced by the so-called Alexiewicz norm (where ) is convex. As a consequence, any such family of Pettis integrable functions is also weakly closed.
A new result of G. A. Edgar on representing points in a convex bounded subset of Banach spaces with the Radon-Nikodym property as barycentres of Radon measures