منابع مشابه
Unconditional Bases and Unconditional Finite-dimensional Decompositions in Banach Spaces
Let X he a Banach space with an unconditional finite-dimensional Schauder decomposition (En). We consider the general problem of characterizing conditions under which one can construct an unconditional basis for X by forming an unconditional basis for each En. For example, we show that if sup,, dim En < c~ and X has Gordon-Lewis local unconditional s t ructure then X has an unconditional basis ...
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A previous article [2] gave results showing that an orthogonal basis which is an unconditional basis for a functional class F furnishes an optimal representation of elements of F for certain de-noising and compression tasks. Since publication of that article, the author received several queries which pointed out that the definition of compression in that article was based on counting the number...
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We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of...
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We prove a general result on complemented unconditional basic sequences in Banach lattices and apply it to give some new examples of spaces with unique unconditional basis. We show that Tsirelson space and certain Nakano spaces have unique unconditional bases. We also construct an example of a space with a unique unconditional basis with a complemented subspace failing to have a unique uncondit...
متن کاملA ug 1 99 4 UNCONDITIONAL BASES AND UNCONDITIONAL FINITE - DIMENSIONAL DECOMPOSITIONS IN BANACH SPACES
Let X be a Banach space with an unconditional finite-dimensional Schauder decomposition (E n). We consider the general problem of characterizing conditions under which one can construct an unconditional basis for X by forming an unconditional basis for each E n. For example, we show that if sup dim E n < ∞ and X has Gordon-Lewis local unconditional structure then X has an unconditional basis of...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1970
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-38-1-248-253