Closed Ideals in Subalgebras of Banach Algebras II: Ditkin's Condition.
Closed ideals in topological algebras: a characterization of the topological -algebra
Let be a uniformly closed and locally m-convex -algebra. We obtain internal conditions on stated in terms of its closed ideals for to be isomorphic and homeomorphic to , the -algebra of all the real continuous functions on a normal topological space endowed with the compact convergence topology.
Closed ideals of A+ and the Cantor set.
Closed ideals with countable hull in algebras of analytic functions smooth up to the boundary.
Closed operator ideals and limiting real interpolation
We establish interpolation properties under limiting real methods for a class of closed ideals including weakly compact operators, Banach-Saks operators, Rosenthal operators and Asplund operators. We show that they behave much better than compact operators.
Closed operators affiliated with a Banach algebra of operators
Let ℬ be a Banach algebra of bounded linear operators on a Banach space X. If S is a closed operator in X such that (λ - S)^{-1} ∈ ℬ for some number λ, then S is affiliated with ℬ. The object of this paper is to study the spectral theory and Fredholm theory relative to ℬ of an operator which is affiliated with ℬ. Also, applications are given to semigroups of operators which are contained in ℬ.
Closed range multipliers and generalized inverses
Conditions involving closed range of multipliers on general Banach algebras are studied. Numerous conditions equivalent to a splitting A = TA ⊕ kerT are listed, for a multiplier T defined on the Banach algebra A. For instance, it is shown that TA ⊕ kerT = A if and only if there is a commuting operator S for which T = TST and S = STS, that this is the case if and only if such S may be taken to be a multiplier, and that these conditions are also equivalent to the existence of a factorization T = PB,...
Closed spectral measures in Fréchet spaces.
Closed subgroups in Banach spaces
We show that zero-dimensional nondiscrete closed subgroups do exist in Banach spaces E. This happens exactly when E contains an isomorphic copy of . Other results on subgroups of linear spaces are obtained.
Closed subgroups of nuclear spaces are weakly closed
Closed universal subspaces of spaces of infinitely differentiable functions
We exhibit the first examples of Fréchet spaces which contain a closed infinite dimensional subspace of universal series, but no restricted universal series. We consider classical Fréchet spaces of infinitely differentiable functions which do not admit a continuous norm. Furthermore, this leads us to establish some more general results for sequences of operators acting on Fréchet spaces with or without a continuous norm. Additionally, we give a characterization of the existence of a closed subspace...
CL-spaces and numerical radius attaining operators.
C-nearest points and the drop property.
Coactions and fell bundles.
Coarea integration in metric spaces
Let be a metric space with a doubling measure, be a boundedly compact metric space and be a Lebesgue precise mapping whose upper gradient belongs to the Lorentz space , . Let be a set of measure zero. Then for -a.e. , where is the -dimensional Hausdorff measure and is the -codimensional Hausdorff measure. This property is closely related to the coarea formula and implies a version of the Eilenberg inequality. The result relies on estimates of Hausdorff content of level sets...
Coarse homology theories.
Cocycle condition for multi-pullbacks of algebras
Take finitely many topological spaces and for each pair of these spaces choose a pair of corresponding closed subspaces that are identified by a homeomorphism. We note that this gluing procedure does not guarantee that the building pieces, or the gluings of some pieces, are embedded in the space obtained by putting together all given ingredients. Dually, we show that a certain sufficient condition, called the cocycle condition, is also necessary to guarantee sheaf-like properties of surjective multi-pullbacks...
Codimension one minimal projections in Banach spaces and a mathematical programming problem [Book]
Coefficient multipliers on spaces of vector-valued entire Dirichlet series
The spaces of entire functions represented by Dirichlet series have been studied by Hussein and Kamthan and others. In the present paper we consider the space of all entire functions defined by vector-valued Dirichlet series and study the properties of a sequence space which is defined using the type of an entire function represented by vector-valued Dirichlet series. The main result concerns with obtaining the nature of the dual space of this sequence space and coefficient multipliers for some...
Coefficient of orthogonal convexity of some Banach function spaces
We study orthogonal uniform convexity, a geometric property connected with property (β) of Rolewicz, P-convexity of Kottman, and the fixed point property (see [19, [20]). We consider the coefficient of orthogonal convexity in Köthe spaces and Köthe-Bochner spaces.