A Criterion for an Operator with Real Spectrum to Be of Scalar-type.
A criterion for compositions of (p,q)-absolutely summing operators to be compact
A criterion for subharmonicity of a function of the spectrum
A criterion of Γ-nullness and differentiability of convex and quasiconvex functions
We introduce a criterion for a set to be Γ-null. Using it we give a shorter proof of the result that the set of points where a continuous convex function on a separable Asplund space is not Fréchet differentiable is Γ-null. Our criterion also implies a new result about Gâteaux (and Hadamard) differentiability of quasiconvex functions.
A curious generalization of local uniform rotundity
A decomposition theorem for regular extensions of von Neumann algebras.
A degree theory for compact perturbations of proper Fredholm mappings of index 0.
A density theorem.
A density theorem for F-spaces
A density theorem for locally convex lattices.
A description of Banach space-valued Orlicz hearts
Let Y be a Banach space, (Ω, Σ; μ) a probability space and φ a finite Young function. It is shown that the Y-valued Orlicz heart H φ(μ, Y) is isometrically isomorphic to the l-completed tensor product of the scalar-valued Orlicz heart Hφ(μ) and Y, in the sense of Chaney and Schaefer. As an application, a characterization is given of the equality of and in terms of the Radon-Nikodým property on Y. Convergence of norm-bounded martingales in H φ(μ, Y) is characterized in terms of the Radon-Nikodým...
A diagonal embedding theorem for function spaces with dominating mixed smoothness properties
A dichotomy on Schreier sets
We show that the Schreier sets have the following dichotomy property. For every hereditary collection ℱ of finite subsets of ℱ, either there exists infinite such that , or there exist infinite such that .
A difference between continuous and absolutely continuous norms in Banach function spaces
On examples we show a difference between a continuous and absolutely continuous norm in Banach function spaces.
A difference quotient norm for spaces of quasi-homogeneous Bessel potentials
A differential equation related to the -norms
Let p ∈ (1,∞). The question of existence of a curve in ℝ₊² starting at (0,0) and such that at every point (x,y) of this curve, the -distance of the points (x,y) and (0,0) is equal to the Euclidean length of the arc of this curve between these points is considered. This problem reduces to a nonlinear differential equation. The existence and uniqueness of solutions is proved and nonelementary explicit solutions are given.
A Differential Inequality for the Distance Function in Normed Linear Spaces.
A Differentiation Theorem for Additive Processes.
A Differentiation Theorem in Lp.
A Dini principle for convex functions and the theorem of James