The Quasiasymptotic Expansion and the Moment Expansion of Tempered Distributions
The quasi-invertible manifold of a JB*-triple.
The Radon measures as functionals on Lipschitz functions
The Radon--Nikodym theorem for reflexive Banach spaces.
The Radon-Nikodym Theorem for Weights on Semi-Finite JBW-Algebras.
The Radon-Nykodym property
The random paving property for uniformly bounded matrices
This note presents a new proof of an important result due to Bourgain and Tzafriri that provides a partial solution to the Kadison-Singer problem. The result shows that every unit-norm matrix whose entries are relatively small in comparison with its dimension can be paved by a partition of constant size. That is, the coordinates can be partitioned into a constant number of blocks so that the restriction of the matrix to each block of coordinates has norm less than one half. The original proof of...
The range of a contractive projection in Lp(H).
We show that the range of a contractive projection on a Lebesgue-Bochner space of Hilbert valued functions Lp(H) is isometric to a lp-direct sum of Hilbert-valued Lp-spaces. We explicit the structure of contractive projections. As a consequence for every 1 < p < ∞ the class Cp of lp-direct sums of Hilbert-valued Lp-spaces is axiomatizable (in the class of all Banach spaces).
The range of a derivation on a Jordan-Banach algebra
The questions when a derivation on a Jordan-Banach algebra has quasi-nilpotent values, and when it has the range in the radical, are discussed.
The range of the Elliott invariant.
The range of Toeplitz operators on the ball.
The range of vector measures into Orlicz spaces
The range of vector valued holomorphic mappings
The real rank of inductive limit C*-algebras.
The realization of positive random variables via absolutely continuous transformations of measure on Wiener space.
The reciprocal Dunford–Pettis property of order in projective tensor products
We investigate whether the projective tensor product of two Banach spaces and has the reciprocal Dunford–Pettis property of order , , when and have the respective property.
The reconstruction of local observable algebras from the euclidean Green's functions of relativistic quantum field theory
The regularity condition for some natural functors
The regularity of convolution and restriction of distributions
The regularity of the positive part of functions in with applications to parabolic equations
Let with be given. Then we show by means of a counter-example that the positive part of has less regularity, in particular it holds in general. Nevertheless, satisfies an integration-by-parts formula, which can be used to prove non-negativity of weak solutions of parabolic equations.