Unitary dilations of commutation relations asscociated to alternating bilinear forms.
It is well known that some dense subspaces of a barrelled space could be not barrelled. Here we prove that dense subspaces of l∞ (Ω, X) are barrelled (unordered Baire-like or p?barrelled) spaces if they have ?enough? subspaces with the considered barrelledness property and if the normed space X has this barrelledness property.These dense subspaces are used in measure theory and its barrelledness is related with some sequences of unitary vectors.
Let be the Hilbert space with reproducing kernel . This paper characterizes some sufficient conditions for a sequence to be a universal interpolating sequence for .
We study analytic families of non-compact cycles, and prove there exists an analytic space of finite dimension, which gives a universal reparametrization of such a family, under some assumptions of regularity. Then we prove an analogous statement for meromorphic families of non-compact cycles. That is a new approach to Grauert’s results about meromorphic equivalence relations.
We show that if a separable Banach space X contains an isometric copy of every strictly convex separable Banach space, then X contains an isometric copy of l1 equipped with its natural norm. In particular, the class of strictly convex separable Banach spaces has no universal element. This provides a negative answer to a question asked by J. Lindenstrauss.
Let X, Y be real Banach spaces and ε > 0. A standard ε-isometry f: X → Y is said to be (α,γ)-stable (with respect to for some α,γ > 0) if T is a linear operator with ||T|| ≤ α such that Tf- Id is uniformly bounded by γε on X. The pair (X,Y) is said to be stable if every standard ε-isometry f: X → Y is (α,γ)-stable for some α,γ > 0. The space X[Y] is said to be universally left [right]-stable if (X,Y) is always stable for every Y[X]. In this paper, we show that universally right-stable...
A generalized approach to several universality results is given by replacing holomorphic or harmonic functions by zero solutions of arbitrary linear partial differential operators. Instead of the approximation theorems of Runge and others, we use an approximation theorem of Hörmander.