Basic sequences in stable infinite type power series spaces
Basis sequences in a stable finite type power series space
Bayoumi Quasi-Differential is different from Fréchet-Differential
We prove that the Quasi Differential of Bayoumi of maps between locally bounded F-spaces may not be Fréchet-Differential and vice versa. So a new concept has been discovered with rich applications (see [1–6]). Our F-spaces here are not necessarily locally convex
Bayoumi quasi-differential is not different from Fréchet-differential
Unlike for Banach spaces, the differentiability of functions between infinite-dimensional nonlocally convex spaces has not yet been properly studied or understood. In a paper published in this Journal in 2006, Bayoumi claimed to have discovered a new notion of derivative that was more suitable for all F-spaces including the locally convex ones with a wider potential in analysis and applied mathematics than the Fréchet derivative. The aim of this short note is to dispel this misconception, since...
Bemerkungen über die Approximationseigenschaft lokalkonvexer Funktionenräume.
Bemerkungen über unendlichdimensionale, separierte Limesvektorräume und Limesgruppen.
Beschränkte Operatoren: Bemerkungen zu einer Arbeit von P. Uss
Bessaga's conjecture in unstable Köthe spaces and products
Let F be a complemented subspace of a nuclear Fréchet space E. If E and F both have (absolute) bases resp. , then Bessaga conjectured (see [2] and for a more general form, also [8]) that there exists an isomorphism of F into E mapping to where is a scalar sequence, π is a permutation of ℕ and is a subsequence of ℕ. We prove that the conjecture holds if E is unstable, i.e. for some base of decreasing zero-neighborhoods consisting of absolutely convex sets one has ∃s ∀p ∃q ∀r where...
Best approximations theorem for a couple in cone Banach space.
Best order conditions in linear spaces, with applications to limitation, inclusion and high indices theorems for ordinary and absolute Riesz means
Bi- convex sets.
Bibounded operators on W*-algebras.
Bicontractive projections in sequence spaces and a few related kinds of maps
Bidual Spaces and Reflexivity of Real Normed Spaces
In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R, real number spaces as real normed spaces and proved related theorems. We can regard linear functionals...
Biduality in (LF)-spaces.
En la Sección 1 se pueban resultados abstractos sobre preduales y sobre bidualidad de espacios (LF). Sea E = indn En un espacio (LF), ponemos H = indn Hn para una sucesión de subespacios de Fréchet Hn de En con Hn ⊂ Hn+1. Investigamos bajo qué condiciones el espacio E es canónicamente (topológicamente isomorfo a) el bidual inductivo (H'b)'i o (incluso) al bidual fuerte de H. Los resultados abstractos se aplican en la Sección 2, especialmente a espacios (LF) ponderados de funciones holomorfas, pero...
Biequivalence vector spaces in the alternative set theory
As a counterpart to classical topological vector spaces in the alternative set theory, biequivalence vector spaces (over the field of all rational numbers) are introduced and their basic properties are listed. A methodological consequence opening a new view towards the relationship between the algebraic and topological dual is quoted. The existence of various types of valuations on a biequivalence vector space inducing its biequivalence is proved. Normability is characterized in terms of total...
Bilinear forms and nuclearity
Bi-locally convex spaces
Biorthogonal systems and bases in Banach space (Preliminary note)
Bolzano’s intermediate-value theorem for quasi-holomorphic maps
We extend Bolzano’s intermediate-value theorem to quasi-holomorphic maps of the space of continuous linear functionals from l p into the scalar field, (0< p<1). This space is isomorphic to l ∞.