Displaying similar documents to “ℱ-bases with brackets and with individual brackets in Banach spaces”

Quotients with a shrinking basis

Jorge Mujica (2012)

Studia Mathematica

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We present a simple proof of a theorem that yields as a corollary a result of Valdivia that sharpens an old result of Johnson and Rosenthal.

Aspects of unconditionality of bases in spaces of compact operators

James R. Holub (1998)

Annales Polonici Mathematici

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E. Tutaj has introduced classes of Schauder bases termed "unconditional-like" (UL) and "unconditional-like*" (UL*) whose intersection is the class of unconditional bases. In view of this association with unconditional bases, it is interesting to note that there exist Banach spaces which have no unconditional basis and yet have a basis of one of these two types (e.g., the space 𝓞[0,1]). In the same spirit, we show in this paper that the space of all compact operators on a reflexive Banach...

Families of almost disjoint Hamel bases.

Lorenz Halbeisen (2005)

Extracta Mathematicae

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For infinite dimensional Banach spaces X we investigate the maximal size of a family of pairwise almost disjoint normalized Hamel bases of X, where two sets A and B are said to be almost disjoint if the cardinality of A ∩ B is smaller than the cardinality of either A or B.

M-bases in spaces of continuous functions on ordinals

Ondrej F. K. Kalenda (2002)

Colloquium Mathematicae

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We prove, among other things, that the space C[0,ω₂] has no countably norming Markushevich basis. This answers a question asked by G. Alexandrov and A. Plichko.