Showing papers on "Dual norm published in 1988"

Characterizations of conditional expectation-type operators

Abstract: As is well-known, conditional expectation operators on various function spaces exhibit a number of remarkable properties related either to the underlying order structure of the given function space, or to the metric structure when the function space is equipped with a norm. Such operators are necessarily positive projections which are averaging in a precise sense to be described below and in certain normed function spaces are contractive for the given norm.

Mixed-norm generalizations of Bergman spaces and duality

Abstract: Conditions sufficient for boundedness of the Bergman projection on certain "mixed-norm" spaces of functions on the unit ball of CN are given, and this is used to identify the dual space of such mixed-norm spaces. Several representation theorems that follow from the duality are also given.

An extension of the Kahane-Khinchine inequality in a Banach space

Abstract: We show that the geometric mean of the norm of a linear combination of the Steinhaus variables with “coefficients” in a Banach space is equivalent to the variance of the norm. This extends a result of Kahane, who established the corresponding inequality for theL p means.

Isometries of some smooth normed spaces of analytic functions

Abstract: Let H(D) denote the linear space of analytic functions on the open unit disc D, and let N be a norm on H(D). Let H N and S N denote the spaces of functions f in H(D) such that respectively. Let H N have the norm N. and give S N norm . We show that when is smooth, the linear isometries of H N can be described in terms of the linear isometries of H N. Applications are given to the weighted Hardy space, the weighted Bergman space, and the Bloch space.

Monotonic norms in ordered banach spaces

Abstract: Let B be an ordered Banach space with ordered Banach dual space. Let N denote the canonical half-norm. We give an alternative proof of the following theorem of Robinson and Yamamuro: the norm on B is a-monotone (a > 1) if and only if for each / in B* there exists g 6 B* with g > 0, / and ||g|| < aN(f). We also establish a dual result characterizing a-monotonicity of B'.

Weighted norm inequalities and uniform algebras

Abstract: Generalizations of the classical conjugation operator can be defined on a general uniform algebra. In this ') paper the L~ weighted problems for the conjugation operators are considered and it is shown that the weights have forms similar to the classical case. The results in this paper have applications to concrete uniform algebras, for example, a polydisC algebra and a uniform algebra which consists of rational functions. §l. Introduction Let X be a compact Hausdorff space, let C(X) be the algebra of complex-valued continuous functions on X, and let A be a uniform algebra on X. Fix a nonzero complex homomorphism T on A and let m be the representing measure for T on X Put A = {f E A ; T(f) = o} o and Co = {f E C(X) ; f Xfdm = o} A uniformly closed subspace is called A-invariant if it is invariant under multiplications by the functions in A. Suppose is a closed invariant subspace in Co For example, such a subspace. It is clear that there exists a largest subspace KO contained in such a closed invariant subspaces, and, in fact, KO = {f E Co . f x£gdm = 0 for all g E A} , The abstract Hardy space HP = HPCm) , / P S.

Differentiability of distance functions in normed linear spaces with uniformly Gateaux differentiable norm

Abstract: Consider a non-empty proper closed subset K of a Banach space $(X, \| \cdot \|)$ where the norm is uniformly Gateaux (uniformly Frechet) differentiable. Then the associated distance function d is guaranteed to be Gateaux differentiable on a dense subset D of X\K. Furthermore, Gateaux (Frechet) differentiability of the distance function at a point $x \in$ X\K can be characterised in terms of the weak* sequences ${d' (x_n)}$ where ${x_n}$ is a sequence in D converging to x.