Search results for "FUNCTIONAL"
showing 10 items of 4822 documents
A unified Pietsch domination theorem
2008
In this paper we prove an abstract version of Pietsch's domination theorem which unify a number of known Pietsch-type domination theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. A final result shows that Pietsch-type dominations are totally free from algebraic conditions, such as linearity, multilinearity, etc.
Finitely randomized dyadic systems and BMO on metric measure spaces
2015
Abstract We study the connection between BMO and dyadic BMO in metric measure spaces using finitely randomized dyadic systems, and give a Garnett–Jones type proof for a theorem of Uchiyama on a construction of certain BMO functions. We obtain a relation between the BMO norm of a suitable expectation over dyadic systems and the dyadic BMO norms of the original functions in different systems. The expectation is taken over only finitely randomized dyadic systems to overcome certain measurability questions. Applying our result, we derive Uchiyama’s theorem from its dyadic counterpart, which we also prove.
On generalized a-Browder's theorem
2007
We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H0(�I T) asbelongs to certain sets of C. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators. 1. Preliminaries. Let L(X) denote the space of bounded linear oper- ators on an infinite-dimensional complex Banach space X. For T ∈ L(X), denote by α(T) the dimension of the kernel ker T, and by β(T) the codi- mension of the range T(X). The operator T ∈ L(X) is called upper semi- Fredholm if α(T) < ∞ and T(X) is closed, and lower …
Injective spaces of real-valued functions with the baire property
1995
Generalizing the technique used by S.A. Argyros in [3], we give a lemma from which certain Banach spaces are shown to be non-injective. This is applied mainly to study the injectivity of spaces of real-valued Borel functions and functions with the Baire property on a topological space. The results obtained in this way do not follow from previous works about this matter.
Boundaries for algebras of analytic functions on function module Banach spaces
2013
We consider the uniform algebra of continuous and bounded functions that are analytic on the interior of the closed unit ball of a complex Banach function module X. We focus on norming subsets of , i.e., boundaries, for such algebra. In particular, if X is a dual complex Banach space whose centralizer is infinite-dimensional, then the intersection of all closed boundaries is empty. This also holds in case that X is an -sum of infinitely many Banach spaces and further, the torus is a boundary.
A Mönch type fixed point theorem under the interior condition
2009
Abstract In this paper we show that the well-known Monch fixed point theorem for non-self mappings remains valid if we replace the Leray–Schauder boundary condition by the interior condition. As a consequence, we obtain a partial generalization of Petryshyn's result for nonexpansive mappings.
Tangency conditions for multivalued mappings
1996
We prove that interiority conditions imply tangency conditions for two multivalued mappings from a topological space into a normed vector space. As a consequence, we obtain the lower semicontinuity of the intersection of two multivalued mappings. An application to the epi-upper semicontinuity of the sum of convex vector-valued mappings is given.
A multilinear Phelps' Lemma
2007
We prove a multilinear version of Phelps' Lemma: if the zero sets of multilinear forms of norm one are 'close', then so are the multilinear forms.
Strict u-ideals in Banach spaces
2009
We study strict u-ideals in Banach spaces. A Banach space X is a strict u-ideal in its bidual when the canonical decomposition X = X X ? is unconditional. We characterize Banach spaces which are strict u-ideals in their bidual and show that if X is a strict u-ideal in a Banach space Y then X contains c0. We also show that '1 is not a u-ideal.
Entire Functions of Bounded Type on Fréchet Spaces
1993
We show that holomorphic mappings of bounded type defined on Frechet spaces extend to the bidual. The relationship between holomorphic mappings of bounded type and of uniformly bounded type is discussed and some algebraic and topological properties of the space of all entire mappings of (uniformly) bounded type are proved, for example a holomorphic version of Schauder's theorem.