König-Witstock quasi-norms on quasi-Banach spaces.
Jesús M. Fernández Castillo, Yolanda Moreno (2002)
Extracta Mathematicae
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Jesús M. Fernández Castillo, Yolanda Moreno (2002)
Extracta Mathematicae
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Fernando Albiac, José Ansorena (2012)
Open Mathematics
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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,...
D. J. Grubb (2008)
Fundamenta Mathematicae
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A quasi-linear map from a continuous function space C(X) is one which is linear on each singly generated subalgebra. We show that the collection of quasi-linear functionals has a Banach space pre-dual with a natural order. We then investigate quasi-linear maps between two continuous function spaces, classifying them in terms of generalized image transformations.
Nigel Kalton (1981)
Studia Mathematica
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Heydar Radjavi, Peter Šemrl (2008)
Studia Mathematica
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Let X and Y be Banach spaces and ℬ(X) and ℬ(Y) the algebras of all bounded linear operators on X and Y, respectively. We say that A,B ∈ ℬ(X) quasi-commute if there exists a nonzero scalar ω such that AB = ωBA. We characterize bijective linear maps ϕ : ℬ(X) → ℬ(Y) preserving quasi-commutativity. In fact, such a characterization can be proved for much more general algebras. In the finite-dimensional case the same result can be obtained without the bijectivity assumption.
N. Kalton (1995)
Studia Mathematica
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We construct a quasi-Banach space X which contains no basic sequence.
Félix Cabello Sánchez (2003)
Fundamenta Mathematicae
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We study the stability of homomorphisms between topological (abelian) groups. Inspired by the "singular" case in the stability of Cauchy's equation and the technique of quasi-linear maps we introduce quasi-homomorphisms between topological groups, that is, maps ω: 𝒢 → ℋ such that ω(0) = 0 and ω(x+y) - ω(x) - ω(y) → 0 (in ℋ) as x,y → 0 in 𝒢. The basic question here is whether ω is approximable by a true homomorphism a in the sense that ω(x)-a(x) → 0...
Wu, Cong, Li, Yongjin (2008)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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J. Ewert (1987)
Matematički Vesnik
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Olivier Olela Otafudu, Zechariah Mushaandja (2017)
Topological Algebra and its Applications
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We show that the image of a q-hyperconvex quasi-metric space under a retraction is q-hyperconvex. Furthermore, we establish that quasi-tightness and quasi-essentiality of an extension of a T0-quasi-metric space are equivalent.
Salvador Romaguera, Michel Schellekens (1998)
Extracta Mathematicae
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B. K. Ray (1978)
Matematički Vesnik
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