An approach to generalizing Banach spaces: normed almost linear spaces
An approximation theorem related to good compact sets in the sense of Martineau
This note contains an approximation theorem that implies that every compact subset of is a good compact set in the sense of Martineau. The property in question is fundamental for the extension of analytic functionals. The approximation theorem depends on a finiteness result about certain polynomially convex hulls.
Asymmetric locally convex spaces.
Bounded Extensions and Characterizations of C(X).
Chain rules for canonical state extensions on von Neumann algebras
In previous papers we introduced and studied the extension of a state defined on a von Neumann subalgebra to the whole of the von Neumann algebra with respect to a given state. This was done by using the standard form of von Neumann algebras. In the case of the existence of a norm one projection from the algebra to the subalgebra preserving the given state our construction is simply equivalent to taking the composition with the norm one projection. In this paper we study couples of von Neumann subalgebras...
Charakterisierung der Quotientenräume von s und eine Vermutung von Martineau
Choice principles in Węglorz’ models
Węglorz' models are models for set theory without the axiom of choice. Each one is determined by an atomic Boolean algebra. Here the algebraic properties of the Boolean algebra are compared to the set theoretic properties of the model.
Common extensions for linear operators
The main meaning of the common extension for two linear operators is the following: given two vector subspaces G₁ and G₂ in a vector space (respectively an ordered vector space) E, a Dedekind complete ordered vector space F and two (positive) linear operators T₁: G₁ → F, T₂: G₂ → F, when does a (positive) linear common extension L of T₁, T₂ exist? First, L will be defined on span(G₁ ∪ G₂). In other results, formulated in the line of the Hahn-Banach extension theorem, the common...
Corrigendum - An approximation theorem related to good compact sets in the sense of Martineau
Deux types nouveaux d'extension de formes linéaires positives et continues
Dual Spaces and Hahn-Banach Theorem
In this article, we deal with dual spaces and the Hahn-Banach Theorem. At the first, we defined dual spaces of real linear spaces and proved related basic properties. Next, we defined dual spaces of real normed spaces. We formed the definitions based on dual spaces of real linear spaces. In addition, we proved properties of the norm about elements of dual spaces. For the proof we referred to descriptions in the article [21]. Finally, applying theorems of the second section, we proved the Hahn-Banach...
Effective determination of all the Hahn--Banach extensions of some linear and continuous functionals.
Egoroff's Theorem
The goal of this article is to prove Egoroff's Theorem [13]. However, there are not enough theorems related to sequence of measurable functions in Mizar Mathematical Library. So we proved many theorems about them. At the end of this article, we showed Egoroff's theorem.MML identifier: MESFUNC8, version: 7.8.10 4.100.1011
Ein Schwach-Stark-Prinzip der Dualitätstheorie lokalkonvexer Räume als Fortsetzungsmethode.
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 of characters in commutative Banach algebras
Extension of linear forms with strict domination on locally compact cones.
Extension of multilinear mappings on Banach spaces
Extensions of convex functionals on convex cones
We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.
Finite dimensional subspaces of