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Representation of the space spanned by a sequence in a Banach space
Archiv der Mathematik, 1984A sequence \((x_ n)\) of a Banach space B is said to be pseudo basic with brackets if there exists an increasing sequence \((q_ n)\) of positive integers so that, setting \(q_ 0=0\), \(x=\sum^{\infty}_{m=0}(\sum^{q_{m+1}}_{n=q_ m+1}a_ nx_ n)\) for every x of \(\overline{span}(x_ n)\), where \((a_ n)\) depends on x while \((q_ n)\) does not depend on x;
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Relative Position, Sequences and Operators in Banach Spaces
Mathematische Nachrichten, 1994This note is a contribution in the research about the relative position of closed subspaces of a Banach space \(B\). In connection with the previous problem, we have among others the following questions: 1) For an \(M\)-basic sequence \((a_i)_{i\in\mathbb{N}}\) of \(B\) the knowledge of the relative position of any two subspaces \([(a_i)_{i\in S ...
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On Relationships Amongst Certain Spaces Of Sequences In An Arbitrary Banach Space
Canadian Journal of Mathematics, 19561. Introduction. Let X be a Banach space (B-space). A sequence {s(i)} in X is unconditionally summable if and only if every rearrangement of the series Σis(i) is convergent. The set of unconditionally summable sequences in X will be written as U(X). In this paper several classes of summable sequences in X will be compared with one another.
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On the geometry of sequences in Banach spaces
Archiv der Mathematik, 1983Plans, Antonio, Reyes, Andres
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Measure of super weak noncompactness in some Banach sequence spaces
Journal of Mathematical Analysis and Applications, 2021Kun Tu
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Subspaces of certain Banach Sequence Spaces
Bulletin of the London Mathematical Society, 1981openaire +2 more sources
On Pitt's Theorem for Operators between Scalar and Vector-Valued Quasi-Banach Sequence Spaces
Monatshefte Fur Mathematik, 2000J A Lopez Molina
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The Banach spaces ℓ∞(c0) and c0(ℓ∞) are not isomorphic
Journal of Mathematical Analysis and Applications, 2010JOSÉ Mendoza
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