Displaying similar documents to “On perfectly homogeneous bases in quasi-Banach spaces.”

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.

A conditional quasi-greedy basis of l₁

S. J. Dilworth, David Mitra (2001)

Studia Mathematica

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We show that the Lindenstrauss basic sequence in l₁ may be used to construct a conditional quasi-greedy basis of l₁, thus answering a question of Wojtaszczyk. We further show that the sequence of coefficient functionals for this basis is not quasi-greedy.

Types of tightness in spaces with unconditional basis

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...

Bayoumi quasi-differential is not different from Fréchet-differential

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,...