On operators from to or to
Christian Samuel (2010)
Colloquium Mathematicae
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We show that every operator from to is compact when 1 ≤ p,q < s and that every operator from to is compact when 1/p + 1/q > 1 + 1/s.
Christian Samuel (2010)
Colloquium Mathematicae
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We show that every operator from to is compact when 1 ≤ p,q < s and that every operator from to is compact when 1/p + 1/q > 1 + 1/s.
Marco Cicalese, Gian Paolo Leonardi (2013)
Journal of the European Mathematical Society
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We prove some results in the context of isoperimetric inequalities with quantitative terms. In the -dimensional case, our main contribution is a method for determining the optimal coefficients in the inequality , valid for each Borel set with positive and finite area, with and being, respectively, the and the of . In dimensions, besides proving existence and regularity properties of minimizers for a wide class of including the lower semicontinuous extension of , we...
Moshe Marcus, Laurent Véron (2004)
Journal of the European Mathematical Society
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Let be a bounded domain of class in N and let be a compact subset of . Assume that and denote by the maximal solution of in which vanishes on . We obtain sharp upper and lower estimates for in terms of the Bessel capacity and prove that is -moderate. In addition we describe the precise asymptotic behavior of at points , which depends on the “density” of at , measured in terms of the capacity .
Václav Kryštof, Luděk Zajíček (2016)
Commentationes Mathematicae Universitatis Carolinae
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It is proved that real functions on which can be represented as the difference of two semiconvex functions with a general modulus (or of two lower -functions, or of two strongly paraconvex functions) coincide with semismooth functions on (i.e. those locally Lipschitz functions on for which and for each ). Further, for each modulus , we characterize the class of functions on which can be written as , where and are semiconvex with modulus (for some ) using a new...
Azam Babai, Zeinab Akhlaghi (2017)
Czechoslovak Mathematical Journal
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Let be a group and be the set of element orders of . Let and be the number of elements of order in . Let nse. Assume is a prime number and let be a group such that nse nse, where is the symmetric group of degree . In this paper we prove that , if divides the order of and does not divide it. To get the conclusion we make use of some well-known results on the prime graphs of finite simple groups and their components.
Paolo Leonetti, Salvatore Tringali (2014)
Journal de Théorie des Nombres de Bordeaux
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Given an integer , let be pairwise coprime integers , a family of nonempty proper subsets of with “enough” elements, and a function . Does there exist at least one prime such that divides for some , but it does not divide ? We answer this question in the positive when the are prime powers and and are subjected to certain restrictions. We use the result to prove that, if and is a set of three or more primes that contains all prime divisors of any...
Abdellatif Chahbi, Samir Kabbaj, Ahmed Charifi (2016)
Mathematica Bohemica
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Let be a complex Hilbert space, a positive operator with closed range in and the sub-algebra of of all -self-adjoint operators. Assume onto itself is a linear continuous map. This paper shows that if preserves -unitary operators such that then defined by is a homomorphism or an anti-homomorphism and for all , where and is the Moore-Penrose inverse of . A similar result is also true if preserves -quasi-unitary operators in both directions such that there...
Hans Triebel (1994)
Studia Mathematica
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Let , where the sum is taken over the lattice of all points k in having integer-valued components, j∈ℕ and . Let be either or (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on The aim of the paper is to clarify under what conditions is equivalent to .
Jacek Dziubański, Jacek Zienkiewicz (2003)
Colloquium Mathematicae
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Let A = -Δ + V be a Schrödinger operator on , d ≥ 3, where V is a nonnegative potential satisfying the reverse Hölder inequality with an exponent q > d/2. We say that f is an element of if the maximal function belongs to , where is the semigroup generated by -A. It is proved that for d/(d+1) < p ≤ 1 the space admits a special atomic decomposition.
Lola Thompson (2014)
Journal de Théorie des Nombres de Bordeaux
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In this paper, we examine a natural question concerning the divisors of the polynomial : “How often does have a divisor of every degree between and ?” In a previous paper, we considered the situation when is factored in . In this paper, we replace with , where is an arbitrary-but-fixed prime. We also consider those where this condition holds for all .
Fabien Durand (2011)
Journal of the European Mathematical Society
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The seminal theorem of Cobham has given rise during the last 40 years to a lot of work about non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the so-called substitutive sequences. Let and be two multiplicatively independent Perron numbers. Then a sequence , where is a finite alphabet, is both -substitutive and -substitutive if and only if is ultimately...
(2016)
Acta Arithmetica
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For n ∈ ℕ, L > 0, and p ≥ 1 let be the largest possible value of k for which there is a polynomial P ≢ 0 of the form , , , such that divides P(x). For n ∈ ℕ, L > 0, and q ≥ 1 let be the smallest value of k for which there is a polynomial Q of degree k with complex coefficients such that . We find the size of and for all n ∈ ℕ, L > 0, and 1 ≤ p,q ≤ ∞. The result about is due to Coppersmith and Rivlin, but our proof is completely different and much shorter even...
Reynaldo Rojas-Hernández (2015)
Commentationes Mathematicae Universitatis Carolinae
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We show that any -product of at most -many -spaces has the -property. This result generalizes some known results about -spaces. On the other hand, we prove that every -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe...
Mariusz Skałba (2003)
Colloquium Mathematicae
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Consider a recurrence sequence of integers satisfying , where are fixed and a₀ ∈ -1,1. Assume that for all sufficiently large k. If there exists k₀∈ ℤ such that then for each negative integer -D there exist infinitely many rational primes q such that for some k ∈ ℕ and (-D/q) = -1.
Binlong Li, Bo Ning (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Let and be two given graphs. The Ramsey number is the least integer such that for every graph on vertices, either contains a or contains a . Parsons gave a recursive formula to determine the values of , where is a path on vertices and is a star on vertices. In this note, we study the Ramsey numbers , where is a linear forest on vertices. We determine the exact values of for the cases and , and for the case that has no odd component. Moreover, we...
Ioana Ghenciu (2017)
Commentationes Mathematicae Universitatis Carolinae
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For Banach spaces and , let denote the space of all continuous compact operators from to endowed with the operator norm. A Banach space has the property if every Grothendieck subset of is relatively weakly compact. In this paper we study Banach spaces with property . We investigate whether the spaces and have the property, when and have the property.
Said Bouali, Youssef Bouhafsi (2015)
Mathematica Bohemica
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Let denote the algebra of operators on a complex infinite dimensional Hilbert space . For , the generalized derivation and the elementary operator are defined by and for all . In this paper, we exhibit pairs of operators such that the range-kernel orthogonality of holds for the usual operator norm. We generalize some recent results. We also establish some theorems on the orthogonality of the range and the kernel of with respect to the wider class of unitarily invariant...