Displaying similar documents to “Fine and quasi connectedness in nonlinear potential theory”

The quasi Isbell topology on function spaces

D. N. Georgiou, A. C. Megaritis (2015)

Colloquium Mathematicae

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In this paper, on the family (Y) of all open subsets of a space Y we define the so called quasi Scott topology, denoted by τ q S c . This topology defines in a standard way, on the set C(Y,Z) of all continuous maps of the space Y to a space Z, a topology t q I s called the quasi Isbell topology. The latter topology is always larger than or equal to the Isbell topology, and smaller than or equal to the strong Isbell topology. Results and problems concerning the topology t q I s are given.

Quasi-constricted linear operators on Banach spaces

Eduard Yu. Emel'yanov, Manfred P. H. Wolff (2001)

Studia Mathematica

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Let X be a Banach space over ℂ. The bounded linear operator T on X is called quasi-constricted if the subspace X : = x X : l i m n | | T x | | = 0 is closed and has finite codimension. We show that a power bounded linear operator T ∈ L(X) is quasi-constricted iff it has an attractor A with Hausdorff measure of noncompactness χ | | · | | ( A ) < 1 for some equivalent norm ||·||₁ on X. Moreover, we characterize the essential spectral radius of an arbitrary bounded operator T by quasi-constrictedness of scalar multiples of T. Finally, we prove...

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 ( ) 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 ( ) l o g N .

Countable compactness and p -limits

Salvador García-Ferreira, Artur Hideyuki Tomita (2001)

Commentationes Mathematicae Universitatis Carolinae

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For M ω * , we say that X is quasi M -compact, if for every f : ω X there is p M such that f ¯ ( p ) X , where 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 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...

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.

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.

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 , . . . , f k : I , k ≥ 2, denoted by A [ f , . . . , f k ] , is considered. Some properties of A [ f , . . . , 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...

Compactness and extreme points of the set of quasi-measure extensions of a quasi-measure

Zbigniew Lipecki

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The memoir is based on a series of six papers by the author published over the years 1995-2007. It continues the work of D. Plachky (1970, 1976). It also owes some inspiration, among others, to papers by J. Łoś and E. Marczewski (1949), D. Bierlein and W. J. A. Stich (1989), D. Bogner and R. Denk (1994), and A. Ülger (1996). Let and ℜ be algebras of subsets of a set Ω with ⊂ ℜ. Given a quasi-measure μ on , i.e., μ ∈ ba₊(), we denote by E(μ) the convex set of all quasi-measure extensions...

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.

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....

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...

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

Similarity:

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.

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 0 , 1 . We prove that for any x ∈ (0,1), (x) contains a sequence β k k 1 increasing to 2. Moreover, (x) is a Lebesgue null set of Hausdorff dimension 1; both (x) and its closure ( x ) ¯ are nowhere dense.

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....

𝔤 -quasi-Frobenius Lie algebras

David N. Pham (2016)

Archivum Mathematicum

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A Lie version of Turaev’s G ¯ -Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a 𝔤 -quasi-Frobenius Lie algebra for 𝔤 a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra ( 𝔮 , β ) together with a left 𝔤 -module structure which acts on 𝔮 via derivations and for which β is 𝔤 -invariant. Geometrically, 𝔤 -quasi-Frobenius Lie algebras are the Lie algebra structures associated to...

Quasi-diffusion solution of a stochastic differential equation

Agnieszka Plucińska, Wojciech Szymański (2007)

Applicationes Mathematicae

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We consider the stochastic differential equation X t = X + 0 t ( A s + B s X s ) d s + 0 t C s d Y s , where A t , B t , C t are nonrandom continuous functions of t, X₀ is an initial random variable, Y = ( Y t , t 0 ) is a Gaussian process and X₀, Y are independent. We give the form of the solution ( X t ) to (0.1) and then basing on the results of Plucińska [Teor. Veroyatnost. i Primenen. 25 (1980)] we prove that ( X t ) is a quasi-diffusion proces.

Iterated quasi-arithmetic mean-type mappings

Paweł Pasteczka (2016)

Colloquium Mathematicae

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We work with a fixed N-tuple of quasi-arithmetic means M , . . . , M N generated by an N-tuple of continuous monotone functions f , . . . , f N : I (I an interval) satisfying certain regularity conditions. It is known [initially Gauss, later Gustin, Borwein, Toader, Lehmer, Schoenberg, Foster, Philips et al.] that the iterations of the mapping I N b ( M ( b ) , . . . , M N ( b ) ) tend pointwise to a mapping having values on the diagonal of I N . Each of [all equal] coordinates of the limit is a new mean, called the Gaussian product of the means M , . . . , M N taken...

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.

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 ) .