The basic sequence problem
N. Kalton (1995)
Studia Mathematica
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We construct a quasi-Banach space X which contains no basic sequence.
N. Kalton (1995)
Studia Mathematica
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We construct a quasi-Banach space X which contains no basic sequence.
Elisabeth Werner (1988)
Mathematische Annalen
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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,...
Nigel Kalton (1981)
Studia Mathematica
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Jesús M. Fernández Castillo, Yolanda Moreno (2002)
Extracta Mathematicae
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J. Achari (1976)
Matematički Vesnik
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Wu, Cong, Li, Yongjin (2008)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Árpád Száz (1998)
Annales Polonici Mathematici
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By introducing the intersection convolution of relations, we prove a natural generalization of an extension theorem of B. Rodrí guez-Salinas and L. Bou on linear selections which is already a substantial generalization of the classical Hahn-Banach theorems. In particular, we give a simple neccesary and sufficient condition in terms of the intersection convolution of a homogeneous relation and its partial linear selections in order that every partial linear selection of this relation...
Seddighin, Morteza (1989)
International Journal of Mathematics and Mathematical Sciences
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B. K. Ray (1978)
Matematički Vesnik
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Félix Cabello Sánchez, Jesús M. F. Castillo, Fernando Sánchez (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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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...
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.
Alistair Bird, Niels Jakob Laustsen (2010)
Banach Center Publications
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We create a new family of Banach spaces, the James-Schreier spaces, by amalgamating two important classical Banach spaces: James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. We then investigate the properties of these James-Schreier spaces, paying particular attention to how key properties of their 'ancestors' (that is, the James space and the Schreier space) are expressed in them. Our main...
Antonis Manoussakis, Anna Pelczar-Barwacz (2014)
Studia Mathematica
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We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal's list related to Gowers' classification program of Banach spaces, but in contrast to the recently constructed space of type (4), our space is also tight with constants, thus essentially extending the list of known examples in Gowers' program. The space is defined on the basis of a boundedly modified mixed Tsirelson space with the use of a special...