Displaying similar documents to “Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces”

Uniqueness of unconditional basis of p ( c ) and p ( ) , 0 < p < 1

F. Albiac, C. Leránoz (2002)

Studia Mathematica

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We prove that the quasi-Banach spaces p ( c ) and p ( ) (0 < p < 1) have a unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss and Tzafriri have previously proved that the same is true for the respective Banach envelopes ( c ) and ℓ₁(ℓ₂). They used duality techniques which are not available in the non-locally convex case.

The universal Banach space with a K -suppression unconditional basis

Taras O. Banakh, Joanna Garbulińska-Wegrzyn (2018)

Commentationes Mathematicae Universitatis Carolinae

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Using the technique of Fraïssé theory, for every constant K 1 , we construct a universal object 𝕌 K in the class of Banach spaces possessing a normalized K -suppression unconditional Schauder basis.

Corrigendum to the paper “The universal Banach space with a K -suppression unconditional basis”

Taras O. Banakh, Joanna Garbulińska-Wegrzyn (2020)

Commentationes Mathematicae Universitatis Carolinae

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We observe that the notion of an almost 𝔉ℑ K -universal based Banach space, introduced in our earlier paper [1]: Banakh T., Garbulińska-Wegrzyn J., The universal Banach space with a K -suppression unconditional basis, Comment. Math. Univ. Carolin. 59 (2018), no. 2, 195–206, is vacuous for K = 1 . Taking into account this discovery, we reformulate Theorem 5.2 from [1] in order to guarantee that the main results of [1] remain valid.

Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms

Liguang Liu, Dachun Yang (2009)

Studia Mathematica

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Let s ∈ ℝ, p ∈ (0,1] and q ∈ [p,∞). It is proved that a sublinear operator T uniquely extends to a bounded sublinear operator from the Triebel-Lizorkin space p , q s ( ) to a quasi-Banach space ℬ if and only if sup | | T ( a ) | | : a is an infinitely differentiable (p,q,s)-atom of p , q s ( ) < ∞, where the (p,q,s)-atom of p , q s ( ) is as defined by Han, Paluszyński and Weiss.

Isomorphisms of some reflexive algebras

Jiankui Li, Zhidong Pan (2008)

Studia Mathematica

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Suppose ℒ₁ and ℒ₂ are subspace lattices on complex separable Banach spaces X and Y, respectively. We prove that under certain lattice-theoretic conditions every isomorphism from algℒ₁ to algℒ₂ is quasi-spatial; in particular, if a subspace lattice ℒ of a complex separable Banach space X contains a sequence E i such that ( E i ) X , E i E i + 1 , and i = 1 E i = X then every automorphism of algℒ is quasi-spatial.

Three-space problems and bounded approximation properties

Wolfgang Lusky (2003)

Studia Mathematica

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Let R n = 1 be a commuting approximating sequence of the Banach space X leaving the closed subspace A ⊂ X invariant. Then we prove three-space results of the following kind: If the operators Rₙ induce basis projections on X/A, and X or A is an p -space, then both X and A have bases. We apply these results to show that the spaces C Λ = s p a n ¯ z k : k Λ C ( ) and L Λ = s p a n ¯ z k : k Λ L ( ) have bases whenever Λ ⊂ ℤ and ℤ∖Λ is a Sidon set.

Some results on quasi-t-dual Baer modules

Rachid Tribak, Yahya Talebi, Mehrab Hosseinpour (2023)

Commentationes Mathematicae Universitatis Carolinae

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Let R be a ring and let M be an R -module with S = End R ( M ) . Consider the preradical Z ¯ for the category of right R -modules Mod- R introduced by Y. Talebi and N. Vanaja in 2002 and defined by Z ¯ ( M ) = { U M : M / U is small in its injective hull } . The module M is called quasi-t-dual Baer if ϕ ϕ ( Z ¯ 2 ( M ) ) is a direct summand of M for every two-sided ideal of S , where Z ¯ 2 ( M ) = Z ¯ ( Z ¯ ( M ) ) . In this paper, we show that M is quasi-t-dual Baer if and only if Z ¯ 2 ( M ) is a direct summand of M and Z ¯ 2 ( M ) is a quasi-dual Baer module. It is also shown that any direct...

On the inclusions of X Φ spaces

Seyyed Mohammad Tabatabaie, Alireza Bagheri Salec (2023)

Mathematica Bohemica

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We give some equivalent conditions (independent from the Young functions) for inclusions between some classes of X Φ spaces, where Φ is a Young function and X is a quasi-Banach function space on a σ -finite measure space ( Ω , 𝒜 , μ ) .

Every separable Banach space has a basis with uniformly controlled permutations

Paolo Terenzi

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There exists a universal control sequence p ̅ ( m ) m = 1 of increasing positive integers such that: Every infinite-dimensional separable Banach space X has a biorthogonal system xₙ,xₙ* with ||xₙ|| = 1 and ||xₙ*|| < K for each n such that, for each x ∈ X, x = n = 1 x π ( n ) * ( x ) x π ( n ) where π(n) is a permutation of n which depends on x but is uniformly controlled by p ̅ ( m ) m = 1 , that is, n n = 1 m π ( n ) n = 1 p ̅ ( m ) n n = 1 p ̅ ( m + 1 ) for each m.

Reflexivity and approximate fixed points

Eva Matoušková, Simeon Reich (2003)

Studia Mathematica

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A Banach space X is reflexive if and only if every bounded sequence xₙ in X contains a norm attaining subsequence. This means that it contains a subsequence x n k for which s u p f S X * l i m s u p k f ( x n k ) is attained at some f in the dual unit sphere S X * . A Banach space X is not reflexive if and only if it contains a normalized sequence xₙ with the property that for every f S X * , there exists g S X * such that l i m s u p n f ( x ) < l i m i n f n g ( x ) . Combining this with a result of Shafrir, we conclude that every infinite-dimensional Banach space contains an unbounded...

From restricted type to strong type estimates on quasi-Banach rearrangement invariant spaces

María Carro, Leonardo Colzani, Gord Sinnamon (2007)

Studia Mathematica

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Let X be a quasi-Banach rearrangement invariant space and let T be an (ε,δ)-atomic operator for which a restricted type estimate of the form T χ E X D ( | E | ) for some positive function D and every measurable set E is known. We show that this estimate can be extended to the set of all positive functions f ∈ L¹ such that | | f | | 1 , in the sense that T f X D ( | | f | | ) . This inequality allows us to obtain strong type estimates for T on several classes of spaces as soon as some information about the galb of the space X is known....

Addendum to "Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105-109)

Aydin Sh. Shukurov (2014)

Colloquium Mathematicae

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It is well known that if φ(t) ≡ t, then the system φ ( t ) n = 0 is not a Schauder basis in L₂[0,1]. It is natural to ask whether there is a function φ for which the power system φ ( t ) n = 0 is a basis in some Lebesgue space L p . The aim of this short note is to show that the answer to this question is negative.

Order convexity and concavity of Lorentz spaces Λ p , w , 0 < p < ∞

Anna Kamińska, Lech Maligranda (2004)

Studia Mathematica

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We study order convexity and concavity of quasi-Banach Lorentz spaces Λ p , w , where 0 < p < ∞ and w is a locally integrable positive weight function. We show first that Λ p , w contains an order isomorphic copy of l p . We then present complete criteria for lattice convexity and concavity as well as for upper and lower estimates for Λ p , w . We conclude with a characterization of the type and cotype of Λ p , w in the case when Λ p , w is a normable space.

Quasi-greedy bases and Lebesgue-type inequalities

S. J. Dilworth, M. Soto-Bajo, V. N. Temlyakov (2012)

Studia Mathematica

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We study Lebesgue-type inequalities for greedy approximation with respect to quasi-greedy bases. We mostly concentrate on the L p spaces. The novelty of the paper is in obtaining better Lebesgue-type inequalities under extra assumptions on a quasi-greedy basis than known Lebesgue-type inequalities for quasi-greedy bases. We consider uniformly bounded quasi-greedy bases of L p , 1 < p < ∞, and prove that for such bases an extra multiplier in the Lebesgue-type inequality can be taken...

On Some Properties of Separately Increasing Functions from [0,1]ⁿ into a Banach Space

Artur Michalak (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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We say that a function f from [0,1] to a Banach space X is increasing with respect to E ⊂ X* if x* ∘ f is increasing for every x* ∈ E. A function f : [ 0 , 1 ] m X is separately increasing if it is increasing in each variable separately. We show that if X is a Banach space that does not contain any isomorphic copy of c₀ or such that X* is separable, then for every separately increasing function f : [ 0 , 1 ] m X with respect to any norming subset there exists a separately increasing function g : [ 0 , 1 ] m such that the sets of...

Order boundedness and weak compactness of the set of quasi-measure extensions of a quasi-measure

Zbigniew Lipecki (2015)

Commentationes Mathematicae Universitatis Carolinae

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Let 𝔐 and be algebras of subsets of a set Ω with 𝔐 , and denote by E ( μ ) the set of all quasi-measure extensions of a given quasi-measure μ on 𝔐 to . We give some criteria for order boundedness of E ( μ ) in b a ( ) , in the general case as well as for atomic μ . Order boundedness implies weak compactness of E ( μ ) . We show that the converse implication holds under some assumptions on 𝔐 , and μ or μ alone, but not in general.

Quasi-completeness on the Spaces of Holomorphic Germs

Roberto Luiz Soraggi (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Sia E uno spazio D F riflessivo e sia K un compatto di E . Si dimostra che lo spazio dei germi olomorfi su K , con la topologia naturale, è un limite induttivo regolare e quasi completo purché lo spazio dei germi olomorfi all'origine sia un limite induttivo regolare.

Order-theoretic properties of some sets of quasi-measures

Zbigniew Lipecki (2017)

Commentationes Mathematicae Universitatis Carolinae

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Let 𝔐 and be algebras of subsets of a set Ω with 𝔐 , and denote by E ( μ ) the set of all quasi-measure extensions of a given quasi-measure μ on 𝔐 to . We show that E ( μ ) is order bounded if and only if it is contained in a principal ideal in b a ( ) if and only if it is weakly compact and extr E ( μ ) is contained in a principal ideal in b a ( ) . We also establish some criteria for the coincidence of the ideals, in b a ( ) , generated by E ( μ ) and extr E ( μ ) .

Sequentially Right Banach spaces of order p

Mahdi Dehghani, Mohammad B. Dehghani, Mohammad S. Moshtaghioun (2020)

Commentationes Mathematicae Universitatis Carolinae

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We introduce and study two new classes of Banach spaces, the so-called sequentially Right Banach spaces of order p , and those defined by the dual property, the sequentially Right * Banach spaces of order p for 1 p . These classes of Banach spaces are characterized by the notions of L p -limited sets in the corresponding dual space and R p * subsets of the involved Banach space, respectively. In particular, we investigate whether the injective tensor product of a Banach space X and a reflexive Banach...

Nearstandardness on a finite set

Lyantse V.

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AbstractLet T be a finite set for which card T is a natural nonstandard number. The linear space T of complex-valued functions on T is nonstandard. For the analysis on T we need a concept of nearstandardness in this space. A version how to introduce such a concept is proposed. Some elementary examples are given. CONTENTSIntroduction.................................................................................................................50. Preliminary notes....................................................................................................7 0.1....

On the Gram-Schmidt orthonormalizatons of subsystems of Schauder systems

Robert E. Zink (2002)

Colloquium Mathematicae

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In one of the earliest monographs that involve the notion of a Schauder basis, Franklin showed that the Gram-Schmidt orthonormalization of a certain Schauder basis for the Banach space of functions continuous on [0,1] is again a Schauder basis for that space. Subsequently, Ciesielski observed that the Gram-Schmidt orthonormalization of any Schauder system is a Schauder basis not only for C[0,1], but also for each of the spaces L p [ 0 , 1 ] , 1 ≤ p < ∞. Although perhaps not probable, the latter...