Isomorphism of certain weak spaces
Denny Leung (1993)
Studia Mathematica
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It is shown that the weak spaces , and are isomorphic as Banach spaces.
Denny Leung (1993)
Studia Mathematica
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It is shown that the weak spaces , and are isomorphic as Banach spaces.
Paul Lewis (1999)
Colloquium Mathematicae
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Bessaga and Pełczyński showed that if embeds in the dual of a Banach space X, then embeds as a complemented subspace of X. Pełczyński proved that every infinite-dimensional closed linear subspace of contains a copy of that is complemented in . Later, Kadec and Pełczyński proved that every non-reflexive closed linear subspace of contains a copy of that is complemented in . In this note a traditional sliding hump argument is used to establish a simple mapping property of...
I. Gasparis, D. Leung (2000)
Studia Mathematica
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It is shown that for every 1 ≤ ξ < ω, two subspaces of the Schreier space generated by subsequences and , respectively, of the natural Schauder basis of are isomorphic if and only if and are equivalent. Further, admits a continuum of mutually incomparable complemented subspaces spanned by subsequences of . It is also shown that there exists a complemented subspace spanned by a block basis of , which is not isomorphic to a subspace generated by a subsequence of ,...
Miklós Laczkovich (1999)
Colloquium Mathematicae
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Let , and . We show that there is a linear operator such that Φ(f)=f a.e. for every , and Φ commutes with all translations. On the other hand, if is a linear operator such that Φ(f)=f for every , then the group = a ∈ ℝ:Φ commutes with the translation by a is of measure zero and, assuming Martin’s axiom, is of cardinality less than continuum. Let Φ be a linear operator from into the space of complex-valued measurable functions. We show that if Φ(f) is non-zero for every ,...
M. Grigorian (1999)
Studia Mathematica
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It is proved that if is a complete orthonormal system of bounded functions and ɛ>0, then there exists a measurable set E ⊂ [0,1] with measure |E|>1-ɛ, a measurable function μ(x), 0 < μ(x) ≤ 1, μ(x) ≡ 1 on E, and a series of the form , where for all q>2, with the following properties: 1. For any p ∈ [1,2) and there are numbers , k=1,2,…, = 1 or 0, such that 2. For every p ∈ [1,2) and there are a function with g(x) = f(x) on E and numbers , k=1,2,…, or 0,...
J. S. Neves (2001)
Bollettino dell'Unione Matematica Italiana
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Il lavoro presenta diverse caratterizzazioni degli spazi Lorentz-Zygmund generalizzati (GLZ) , con , , e spazio misurato con misura finita. Dato uno spazio misurato e , otteniamo representazioni equivalenti per la (quasi-) norma dello spazio GLZ . Inoltre, se è uno spazio misurato con misura finita e , viene presentata in termini di decomposizioni una norma equivalente per lo spazio . Si dimostra che le norme equivalenti considerate per , con uno spazio a misura...
Vassiliki Farmaki (1993)
Studia Mathematica
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For every element x** in the double dual of a separable Banach space X there exists the sequence of the canonical reproductions of x** in the even-order duals of X. In this paper we prove that every such sequence defines a spreading model for X. Using this result we characterize the elements of X**╲ X which belong to the class (resp. to the class ) as the elements with the sequence equivalent to the usual basis of (resp. as the elements with the sequence equivalent to the...
P. Enflo, T. Starbird (1979)
Studia Mathematica
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Jean-Loup Mauclaire (2000)
Journal de théorie des nombres de Bordeaux
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Let , be a Cantor scale, the compact projective limit group of the groups , identified to , and let be its normalized Haar measure. To an element , of we associate the sequence of integral valued random variables . The main result of this article is that, given a complex -multiplicative function of modulus , we have
Jürgen Batt, Georg Schlüchtermann (1986)
Studia Mathematica
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T. Figiel, T. Iwaniec, A. Pełczyński (1984)
Studia Mathematica
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