Examples on Projective Spectra of (LB)-spaces.
Excision in entire cyclic cohomology
We prove that entire and periodic cyclic cohomology satisfy excision for extensions of bornological algebras with a bounded linear section. That is, for such an extension we obtain a six term exact sequence in cohomology.
Exhaustive measures in arbitrary topological vector spaces
Exhaustivity in Topological Riesz Spaces with the Principal Projection Property
Exhaustive and uniformly exhaustive elements are studied in the setting of locally solid topological Riesz spaces with the principal projection property. We study the structure of the order interval [0,x] when x is an exhaustive element and the structure of the solid hull of a set of uniformly exhaustive elements.
Existence and integral representation of regular extensions of measures
Let ℒ be a δ-lattice in a set X, and let ν be a measure on a sub-σ-algebra of σ(ℒ). It is shown that ν extends to an ℒ-regular measure on σ(ℒ) provided ν*|ℒ is σ-smooth at ∅ and ν*(L) = inf ν*(U)|X ∖ U ∈ ℒ, Usupset L for all L ∈ ℒ. Moreover, a Choquet type representation theorem is proved for the set of all such extensions.
Existence of bases and the dual splitting relation for Fréchet spaces
Existence of best approximations
Existence of open quasiconvex subsets dense in a given space
Exposed Points of the Unit Ball of ...(H).
Extending a Norm from a Vector Lattice to its Dedekind Completion.
Extending and lifting some linear topological structures.
Extension and splitting theorems for Fréchet spaces of type 2.
We prove the following common generalization of Maurey's extension theorem and Vogt's (DN)-(Omega) splitting theorem for Fréchet spaces: if T is an operator from a subspace E of a Fréchet space G of type 2 to a Fréchet space F of dual type 2, then T extends to a map from G into F'' whenever G/E satisfies (DN) and F satisfies (Omega).
Extension maps in ultradifferentiable and ultraholomorphic function spaces
The problem of the existence of extension maps from 0 to ℝ in the setting of the classical ultradifferentiable function spaces has been solved by Petzsche [9] by proving a generalization of the Borel and Mityagin theorems for -spaces. We get a Ritt type improvement, i.e. from 0 to sectors of the Riemann surface of the function log for spaces of ultraholomorphic functions, by first establishing a generalization to some nonclassical ultradifferentiable function spaces.
Extension of characters in commutative Banach algebras
Extension of Continuous Functionals
Extension of linear forms with strict domination on locally compact cones.
Extension of measures and integrals by the help of a pseudometric
Extension of multilinear mappings on Banach spaces
Extension of sequentially continuous functionals in inductive limits of Banach spaces
Extension of vector-valued holomorphic and harmonic functions
We present a unified approach to the study of extensions of vector-valued holomorphic or harmonic functions based on the existence of weak or weak*-holomorphic or harmonic extensions. Several recent results due to Arendt, Nikolski, Bierstedt, Holtmanns and Grosse-Erdmann are extended. An open problem by Grosse-Erdmann is solved in the negative. Using the extension results we prove existence of Wolff type representations for the duals of certain function spaces.