Displaying similar documents to “On the structure of Banach spaces with an unconditional basic sequence”

Subspaces of ℓ₂(X) and Rad(X) without local unconditional structure

Ryszard A. Komorowski, Nicole Tomczak-Jaegermann (2002)

Studia Mathematica

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It is shown that if a Banach space X is not isomorphic to a Hilbert space then the spaces ℓ₂(X) and Rad(X) contain a subspace Z without local unconditional structure, and therefore without an unconditional basis. Moreover, if X is of cotype r < ∞, then a subspace Z of ℓ₂(X) can be constructed without local unconditional structure but with 2-dimensional unconditional decomposition, hence also with basis.

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...