On the points of multivaluedness of monotone operators
On the positive projection constant
On the positivity of the unit element in a normed lattice ordered algebra
On the principle of local reflexivity
We prove a version of the local reflexivity theorem which is, in a sense, the most general one: our main theorem characterizes the conditions which can be imposed additionally on the usual local reflexivity map provided that these conditions are of a certain general type. It is then shown how known and new local reflexivity theorems can be derived. In particular, the compatibility of the local reflexivity map with subspaces and operators is investigated.
On the problem of retracting balls onto their boundary.
On the projection constants of some topological spaces and some applications.
On the quasi-weak drop property
A new drop property, the quasi-weak drop property, is introduced. Using streaming sequences introduced by Rolewicz, a characterisation of the quasi-weak drop property is given for closed bounded convex sets in a Fréchet space. From this, it is shown that the quasi-weak drop property is equivalent to weak compactness. Thus a Fréchet space is reflexive if and only if every closed bounded convex set in the space has the quasi-weak drop property.
On the Rademacher maximal function
This paper studies a new maximal operator introduced by Hytönen, McIntosh and Portal in 2008 for functions taking values in a Banach space. The -boundedness of this operator depends on the range space; certain requirements on type and cotype are present for instance. The original Euclidean definition of the maximal function is generalized to σ-finite measure spaces with filtrations and the -boundedness is shown not to depend on the underlying measure space or the filtration. Martingale techniques...
On the Radon-Nikodym property in locally convex spaces and the completeness of L1ε.
On the randomized complexity of Banach space valued integration
We study the complexity of Banach space valued integration in the randomized setting. We are concerned with r times continuously differentiable functions on the d-dimensional unit cube Q, with values in a Banach space X, and investigate the relation of the optimal convergence rate to the geometry of X. It turns out that the nth minimal errors are bounded by if and only if X is of equal norm type p.
On the range of the derivative of a real-valued function with bounded support
We study the set f’(X) = f’(x): x ∈ X when f:X → ℝ is a differentiable bump. We first prove that for any C²-smooth bump f: ℝ² → ℝ the range of the derivative of f must be the closure of its interior. Next we show that if X is an infinite-dimensional separable Banach space with a -smooth bump b:X → ℝ such that is finite, then any connected open subset of X* containing 0 is the range of the derivative of a -smooth bump. We also study the finite-dimensional case which is quite different. Finally,...
On the relation between ordered sets and Lorentz--Minkowski distances in real inner product spaces.
On the relation between several notions of unconditional structure - A counterexample
On the relation of the bounded approximation property and a finite dimensional decomposition in nuclear Fréchet spaces
On the Relationship Between yp-Radonifying Operators and Other Operator Ideals in Banach Spaces of Stable Type p.
On the relationships between Hp(T,X/Y) and Hp(T,X)/ Hp(T,Y).
On the Representation of Banach Lattices by Continuous Numerical Functions.
On the representation of uncountable symmetric basic sets and its applications
It is shown that every uncountable symmetric basic set in an F-space with a symmetric basis is equivalent to a basic set generated by one vector. We apply this result to investigate the structure of uncountable symmetric basic sets in Orlicz and Lorentz spaces.
On the Riesz-Fischer theorem in a smooth Banach space
On the separation of closed, convex sets