Search results for " function"

showing 10 items of 9395 documents

On operator valued sequences of multipliers and R-boundedness

2007

AbstractIn recent papers (cf. [J.L. Arregui, O. Blasco, (p,q)-Summing sequences, J. Math. Anal. Appl. 274 (2002) 812–827; J.L. Arregui, O. Blasco, (p,q)-Summing sequences of operators, Quaest. Math. 26 (2003) 441–452; S. Aywa, J.H. Fourie, On summing multipliers and applications, J. Math. Anal. Appl. 253 (2001) 166–186; J.H. Fourie, I. Röntgen, Banach space sequences and projective tensor products, J. Math. Anal. Appl. 277 (2) (2003) 629–644]) the concept of (p,q)-summing multiplier was considered in both general and special context. It has been shown that some geometric properties of Banach spaces and some classical theorems can be described using spaces of (p,q)-summing multipliers. The p…

Discrete mathematicsSemi-Rademacher boundedApplied MathematicsLinear operatorsBanach spaceWeakly Rademacher boundedMultiplier (Fourier analysis)Linear mapTensor productOperator (computer programming)Multiplier sequenceBounded functionAlmost summingProjective space(pq)-Summing multiplierRademacher bounded sequenceAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Isometries of weighted spaces of holomorphic functions on unbounded domains

2009

We study isometries between weighted spaces of holomorphic functions on unbounded domains in ℂn. We show that weighted spaces of holomorphic functions on unbounded domains may exhibit behaviour different from that observed on bounded domains. We calculate the isometries for specific weights on the complex plane and the right half-plane.

Discrete mathematicsSemi-infiniteGeneral MathematicsBounded functionHolomorphic functionComplex planeMathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
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Characterizing varieties of colength ≤4

2009

Let A be an associative algebra over a field F of characteristic zero, and let χ n (A), n = 1,2,…, be the sequence of cocharacters of A. For every n ≥ 1, let l n (A) denote the nth colength of A, counting the number of S n -irreducibles appearing in χ n (A). In this article, we classify the algebras A such that the sequence of colengths l n (A), n = 1,2,…, is bounded by four. Moreover we construct a finite number of algebras A 1,…, A d , such that l n (A) ≤ 4 if and only if A 1,…, A d  ∉ var(A).

Discrete mathematicsSequenceAlgebra and Number TheoryZero (complex analysis)Field (mathematics)Codimensions; Colengths; Polynomial identity; VarietyPolynomial identitySettore MAT/02 - AlgebraBounded functionCodimensionAssociative algebraVarietyColengthVariety (universal algebra)Finite setMathematics
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Internal inverse limits and retractions

2015

We establish equivalences between compacta that admit a sequence of retractions that converge uniformly to the identity map and compacta that are inverse limits on subcompacta with retractions for bonding maps. We give partial answers to questions of Charatonik and Prajs, and of Krasinkiewicz. Our results are related to and use results from another paper of the authors \cite{mp}.

Discrete mathematicsSequenceGeneral Mathematics54A20Inverse$r$-maps54F6554C15retractions54F15CalculusIdentity functionInternal inverse limitMathematics
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Varieties of superalgebras of almost polynomial growth

2011

Abstract Let V gr be a variety of superalgebras and let c n gr ( V gr ) , n = 1 , 2 , …  , be its sequence of graded codimensions. Such a sequence is polynomially bounded if and only if V gr does not contain a list of five superalgebras consisting of a commutative superalgebra, the infinite dimensional Grassmann algebra and the algebra of 2 × 2 upper triangular matrices with trivial and natural Z 2 -gradings. In this paper we completely classify all subvarieties of the varieties generated by these five superalgebras, by giving a complete list of finite dimensional generating superalgebras.

Discrete mathematicsSequencePolynomialPure mathematicsAlgebra and Number TheoryMathematics::Rings and AlgebrasTriangular matrixGrowthPolynomial identitySuperalgebrasuperalgebra growthBounded functionMathematics::Quantum AlgebraVarietyVariety (universal algebra)Mathematics::Representation TheoryExterior algebraCommutative propertyMathematicsJournal of Algebra
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Polynomial identities on superalgebras and exponential growth

2003

Abstract Let A be a finitely generated superalgebra over a field F of characteristic 0. To the graded polynomial identities of A one associates a numerical sequence {cnsup(A)}n⩾1 called the sequence of graded codimensions of A. In case A satisfies an ordinary polynomial identity, such sequence is exponentially bounded and we capture its exponential growth by proving that for any such algebra lim n→∞ c n sup (A) n exists and is a non-negative integer; we denote such integer by supexp(A) and we give an effective way for computing it. As an application, we construct eight superalgebras Ai, i=1,…,8, characterizing the identities of any finitely generated superalgebra A with supexp(A)>2 in the f…

Discrete mathematicsSequencePolynomialSuperalgebrasAlgebra and Number TheoryMathematics::Rings and AlgebrasField (mathematics)GrowthSuperalgebraCodimensionsPolynomial identitiesIdentity (mathematics)IntegerBounded functionIdeal (ring theory)MathematicsJournal of Algebra
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Proper identities, Lie identities and exponential codimension growth

2008

Abstract The exponent exp ( A ) of a PI-algebra A in characteristic zero is an integer and measures the exponential rate of growth of the sequence of codimensions of A [A. Giambruno, M. Zaicev, On codimension growth of finitely generated associative algebras, Adv. Math. 140 (1998) 145–155; A. Giambruno, M. Zaicev, Exponential codimension growth of P.I. algebras: An exact estimate, Adv. Math. 142 (1999) 221–243]. In this paper we study the exponential rate of growth of the sequences of proper codimensions and Lie codimensions of an associative PI-algebra. We prove that the corresponding proper exponent exists for all PI-algebras, except for some algebras of exponent two strictly related to t…

Discrete mathematicsSequencePure mathematicsAlgebra and Number TheoryZero (complex analysis)CodimensionExponential functionPolynomial identitiesIntegerpolynomial identity codimensionsExponentCodimension growthExterior algebraAssociative propertyMathematics
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Absolutely summing operators on C[0,1] as a tree space and the bounded approximation property

2010

Abstract Let X be a Banach space. For describing the space P ( C [ 0 , 1 ] , X ) of absolutely summing operators from C [ 0 , 1 ] to X in terms of the space X itself, we construct a tree space l 1 tree ( X ) on X. It consists of special trees in X which we call two-trunk trees. We prove that P ( C [ 0 , 1 ] , X ) is isometrically isomorphic to l 1 tree ( X ) . As an application, we characterize the bounded approximation property (BAP) and the weak BAP in terms of X ∗ -valued sequence spaces.

Discrete mathematicsSequenceTree (descriptive set theory)Approximation propertyBounded functionInfinite-dimensional vector functionBanach spaceSpace (mathematics)Operator spaceAnalysisMathematicsJournal of Functional Analysis
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On n–Fold Blocking Sets

1986

An n-fold blocking set is a set of n-disjoint blocking sets. We shall prove upper and lower bounds for the number of components in an n-fold blocking set in projective and affine spaces.

Discrete mathematicsSet (abstract data type)CombinatoricsQuantitative Biology::BiomoleculesSteiner systemBlocking setFold (higher-order function)Blocking (radio)Projective planeAffine transformationUpper and lower boundsMathematics
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Probabilistic entailment and iterated conditionals

2020

In this paper we exploit the notions of conjoined and iterated conditionals, which are defined in the setting of coherence by means of suitable conditional random quantities with values in the interval $[0,1]$. We examine the iterated conditional $(B|K)|(A|H)$, by showing that $A|H$ p-entails $B|K$ if and only if $(B|K)|(A|H) = 1$. Then, we show that a p-consistent family $\mathcal{F}=\{E_1|H_1,E_2|H_2\}$ p-entails a conditional event $E_3|H_3$ if and only if $E_3|H_3=1$, or $(E_3|H_3)|QC(\mathcal{S})=1$ for some nonempty subset $\mathcal{S}$ of $\mathcal{F}$, where $QC(\mathcal{S})$ is the quasi conjunction of the conditional events in $\mathcal{S}$. Then, we examine the inference rules $A…

Discrete mathematicsSettore MAT/06 - Probabilita' E Statistica MatematicaIterated functionInterval (graph theory)Settore MAT/01 - Logica MatematicaCoherence Conditional random quantities p-entailment Inference rules.MathematicsStrict conditional
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