A remark on Rainwater's theorem.
A remark on reflexivity and summability
A remark on the multipliers of the Haar basis of L¹[0,1]
A proof of a necessary and sufficient condition for a sequence to be a multiplier of the normalized Haar basis of L¹[0,1] is given. This proof depends only on the most elementary properties of this system and is an alternative proof to that recently found by Semenov & Uksusov (2012). Additionally, representations are given, which use stochastic processes, of this multiplier norm and of related multiplier norms.
A remark on Ʌ-systems in Banach spaces
A renorming of , rare but with the fixed-point property.
A representation theorem for
A representation theorem for the second dual of C[0,1]
A restricted form of the theorem of Maurey-Pisier for the cotype in -Banach spaces
A result of Haydon and its applications
A result on the isomorphic embeddability of l¹(Γ)
A series whose sum range is an arbitrary finite set
In finite-dimensional spaces the sum range of a series has to be an affine subspace. It has long been known that this is not the case in infinite-dimensional Banach spaces. In particular in 1984 M. I. Kadets and K. Woźniakowski obtained an example of a series whose sum range consisted of two points, and asked whether it was possible to obtain more than two, but finitely many points. This paper answers this question affirmatively, by showing how to obtain an arbitrary finite set as the sum range...
A short proof of Dvoretzky's theorem
A short proof on lifting of projection properties in Riesz spaces
Let be an Archimedean Riesz space with a weak order unit . A sufficient condition under which Dedekind [-]completeness of the principal ideal can be lifted to is given (Lemma). This yields a concise proof of two theorems of Luxemburg and Zaanen concerning projection properties of -spaces. Similar results are obtained for the Riesz spaces , , of all functions of the th Baire class on a metric space .
A short remark on Kolmogoroff normability theorem.
A simple formula showing L¹ is a maximal overspace for two-dimensional real spaces
It follows easily from a result of Lindenstrauss that, for any real twodimensional subspace v of L¹, the relative projection constant λ(v;L¹) of v equals its (absolute) projection constant . The purpose of this paper is to recapture this result by exhibiting a simple formula for a subspace V contained in and isometric to v and a projection from C ⊕ V onto V such that , where P₁ is a minimal projection from L¹(ν) onto v. Specifically, if , then , where and .
A simple observation about compactness and fast decay of Fourier coefficients.
A simple proof of a result of Abramovich and Wickstead
The paper presents a simple proof of Proposition 8 of [2], based on a new and simple description of isometries between CD 0-spaces.
A Simple Proof of the Dauns-Hofmann Theorem.
A simple proof of two theorems concerning bases of
A simplification in the proof of the non-isomorphism between H¹(δ) and H¹(δ²)
The proof that H¹(δ) and H¹(δ²) are not isomorphic is simplified. This is done by giving a new and simple proof to a martingale inequality of J. Bourgain.