Quasi-constricted linear operators on Banach spaces

Eduard Yu. Emel'yanov; Manfred P. H. Wolff

Displaying similar documents to “Quasi-constricted linear operators on Banach spaces”

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 $Ḟ_{p, q}^{s} (ℝ ⁿ)$ to a quasi-Banach space ℬ if and only if sup ${| | T (a) | |}_{ℬ}$ : a is an infinitely differentiable (p,q,s)-atom of $Ḟ_{p, q}^{s} (ℝ ⁿ)$ < ∞, where the (p,q,s)-atom of $Ḟ_{p, q}^{s} (ℝ ⁿ)$ is as defined by Han, Paluszyński and Weiss.

Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces

F. Albiac, J. L. Ansorena, G. Garrigós, E. Hernández, M. Raja (2015)

Studia Mathematica

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We show that in a super-reflexive Banach space, the conditionality constants $k_{N} (ℬ)$ of a quasi-greedy basis ℬ grow at most like $O ({(l o g N)}^{1 - ε})$ for some 0 < ε < 1. This extends results by the third-named author and Wojtaszczyk (2014), where this property was shown for quasi-greedy bases in $L_{p}$ for 1 < p < ∞. We also give an example of a quasi-greedy basis ℬ in a reflexive Banach space with $k_{N} (ℬ) \approx l o g N$ .

Norm convergence of some power series of operators in $L^{p}$ with applications in ergodic theory

Christophe Cuny (2010)

Studia Mathematica

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Let X be a closed subspace of $L^{p} (μ)$ , where μ is an arbitrary measure and 1 < p < ∞. Let U be an invertible operator on X such that $s u p_{n \in ℤ} | | U ⁿ | | < \infty$ . Motivated by applications in ergodic theory, we obtain (optimal) conditions for the convergence of series like $\sum_{n \geq 1} (U ⁿ f) / n^{1 - α}$ , 0 ≤ α < 1, in terms of $| | f + \dots + U^{n - 1} f {| |}_{p}$ , generalizing results for unitary (or normal) operators in L²(μ). The proofs make use of the spectral integration initiated by Berkson and Gillespie and, more particularly, of results from a paper by Berkson-Bourgain-Gillespie. ...

Fine and quasi connectedness in nonlinear potential theory

David R. Adams, John L. Lewis (1985)

Annales de l'institut Fourier

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If $B_{α, p}$ denotes the Bessel capacity of subsets of Euclidean $n$ -space, $α > 0$ , $1 < p < \infty$ , naturally associated with the space of Bessel potentials of $L^{p}$ -functions, then our principal result is the estimate: for $1 < α p \leq n$ , there is a constant $C = C (α, p, n)$ such that for any set $E$ $min {B_{α, p} (E \cap Q), B_{α, p} (E^{c} \cap Q)} \leq C \cdot B_{α, p} (Q \cap \partial_{f} E)$ for all open cubes $Q$ in $n$ -space. Here $\partial_{f} E$ is the boundary of the $E$ in the $(α, p)$ -fine topology i.e. the smallest topology on $c$ -space that makes the associated $(α, p)$ -linear potentials continuous there. As a consequence,...

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 $\bar{Z}$ for the category of right $R$ -modules Mod- $R$ introduced by Y. Talebi and N. Vanaja in 2002 and defined by $\bar{Z} (M) = ⋂ {U \leq M : M / U$ is small in its injective hull $}$ . The module $M$ is called quasi-t-dual Baer if $\sum_{ϕ \in ℑ} ϕ ({\bar{Z}}^{2} (M))$ is a direct summand of $M$ for every two-sided ideal $ℑ$ of $S$ , where ${\bar{Z}}^{2} (M) = \bar{Z} (\bar{Z} (M))$ . In this paper, we show that $M$ is quasi-t-dual Baer if and only if ${\bar{Z}}^{2} (M)$ is a direct summand of $M$ and ${\bar{Z}}^{2} (M)$ is a quasi-dual Baer module. It is also shown that any direct...

Quasi-algebraic representability of sets in $R^{n}$ .

W. Waliszewski (1984)

Banach Center Publications

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Generalized weighted quasi-arithmetic means and the Kolmogorov-Nagumo theorem

Janusz Matkowski (2013)

Colloquium Mathematicae

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A generalization of the weighted quasi-arithmetic mean generated by continuous and increasing (decreasing) functions $f ₁, . . ., f_{k} : I \to ℝ$ , k ≥ 2, denoted by $A^{[f ₁, . . ., f_{k}]}$ , is considered. Some properties of $A^{[f ₁, . . ., f_{k}]}$ , including “associativity” assumed in the Kolmogorov-Nagumo theorem, are shown. Convex and affine functions involving this type of means are considered. Invariance of a quasi-arithmetic mean with respect to a special mean-type mapping built of generalized means is applied in solving a functional equation. For...

An inconsistency equation involving means

Roman Ger, Tomasz Kochanek (2009)

Colloquium Mathematicae

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We show that any quasi-arithmetic mean $A_{φ}$ and any non-quasi-arithmetic mean M (reasonably regular) are inconsistent in the sense that the only solutions f of both equations $f (M (x, y)) = A_{φ} (f (x), f (y))$ and $f (A_{φ} (x, y)) = M (f (x), f (y))$ are the constant ones.

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 $(Ω, 𝒜, μ)$ .

Univoque sets for real numbers

Fan Lü, Bo Tan, Jun Wu (2014)

Fundamenta Mathematicae

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For x ∈ (0,1), the univoque set for x, denoted (x), is defined to be the set of β ∈ (1,2) such that x has only one representation of the form x = x₁/β + x₂/β² + ⋯ with $x_{i} \in 0, 1$ . We prove that for any x ∈ (0,1), (x) contains a sequence ${β_{k}}_{k \geq 1}$ increasing to 2. Moreover, (x) is a Lebesgue null set of Hausdorff dimension 1; both (x) and its closure $\bar{(x)}$ are nowhere dense.

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 $(E_{i}) ₋ \neq X$ , $E_{i} \subseteq E_{i + 1}$ , and $⋁_{i = 1}^{\infty} E_{i} = X$ then every automorphism of algℒ is quasi-spatial.

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 $ℂ^{T}$ of complex-valued functions on T is nonstandard. For the analysis on $ℂ^{T}$ 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....

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 $∥ T χ_{E} ∥_{X} \leq D (| E |)$ 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 ${| | f | |}_{\infty} \leq 1$ , in the sense that $∥ T f ∥_{X} \leq D (| | f | | ₁)$ . 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....

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 Lincei. Matematica e Applicazioni

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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 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 $ℜ$ be algebras of subsets of a set $Ω$ with $𝔐 \subset ℜ$ , and denote by $E (μ)$ the set of all quasi-measure extensions of a given quasi-measure $μ$ on $𝔐$ to $ℜ$ . We give some criteria for order boundedness of $E (μ)$ in $b a (ℜ)$ , 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 $𝔐$ , $ℜ$ and $μ$ or $μ$ alone, but not in general.

Countable compactness and $p$ -limits

Salvador García-Ferreira, Artur Hideyuki Tomita (2001)

Commentationes Mathematicae Universitatis Carolinae

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For $\emptyset \neq M \subseteq ω^{*}$ , we say that $X$ is quasi $M$ -compact, if for every $f : ω \to X$ there is $p \in M$ such that $\bar{f} (p) \in X$ , where $\bar{f}$ is the Stone-Čech extension of $f$ . In this context, a space $X$ is countably compact iff $X$ is quasi $ω^{*}$ -compact. If $X$ is quasi $M$ -compact and $M$ is either finite or countable discrete in $ω^{*}$ , then all powers of $X$ are countably compact. Assuming $C H$ , we give an example of a countable subset $M \subseteq ω^{*}$ and a quasi $M$ -compact space $X$ whose square is not countably compact, and show that in a model of A. Blass and S. Shelah...