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ℱ-bases with brackets and with individual brackets in Banach spaces

Tomasz Kochanek (2012)

Studia Mathematica

We provide a partial answer to the question of Vladimir Kadets whether given an ℱ-basis of a Banach space X, with respect to some filter ℱ ⊂ 𝒫(ℕ), the coordinate functionals are continuous. The answer is positive if the character of ℱ is less than 𝔭. In this case every ℱ-basis is an M-basis with brackets which are determined by an element of ℱ.

Basic relations valid for the Bernstein spaces B ² σ and their extensions to larger function spaces via a unified distance concept

P. L. Butzer, R. L. Stens, G. Schmeisser (2014)

Banach Center Publications

Some basic theorems and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces B σ p are no longer valid in larger spaces. However, when a function f is in some sense close to a Bernstein space, then the corresponding relation holds with a remainder or error term. This paper presents a new, unified approach to these errors in terms of the distance of f from B σ p . The difficult situation of derivative-free error estimates is also covered.

Bayoumi Quasi-Differential is different from Fréchet-Differential

Aboubakr Bayoumi (2006)

Open Mathematics

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

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