Displaying similar documents to “On isomorphic classification of tensor products E ( a ) ̂ E ' ( b )

Isomorphisms of Cartesian Products of ℓ-Power Series Spaces

E. Karapınar, M. Yurdakul, V. Zahariuta (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let ℓ be a Banach sequence space with a monotone norm · , in which the canonical system ( e i ) is a normalized symmetric basis. We give a complete isomorphic classification of Cartesian products E 0 ( a ) × E ( b ) where E 0 ( a ) = K ( e x p ( - p - 1 a i ) ) and E ( b ) = K ( e x p ( p a i ) ) are finite and infinite ℓ-power series spaces, respectively. This classification is the generalization of the results by Chalov et al. [Studia Math. 137 (1999)] and Djakov et al. [Michigan Math. J. 43 (1996)] by using the method of compound linear topological invariants developed by...

Equicontinuity and Convergent Sequences in the Spaces C ' and M

Jan Kisyński (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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Characterizations of equicontinuity and convergent sequences are given for the space C ' ( ) of rapidly decreasing distributions and the space M ( ) of slowly increasing infinitely differentiable functions.

Duality of matrix-weighted Besov spaces

Svetlana Roudenko (2004)

Studia Mathematica

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We determine the duals of the homogeneous matrix-weighted Besov spaces p α q ( W ) and p α q ( W ) which were previously defined in [5]. If W is a matrix A p weight, then the dual of p α q ( W ) can be identified with p ' - α q ' ( W - p ' / p ) and, similarly, [ p α q ( W ) ] * p ' - α q ' ( W - p ' / p ) . Moreover, for certain W which may not be in the A p class, the duals of p α q ( W ) and p α q ( W ) are determined and expressed in terms of the Besov spaces p ' - α q ' ( A Q - 1 ) and p ' - α q ' ( A Q - 1 ) , which we define in terms of reducing operators A Q Q associated with W. We also develop the basic theory of these reducing operator Besov spaces....

On Fourier asymptotics of a generalized Cantor measure

Bérenger Akon Kpata, Ibrahim Fofana, Konin Koua (2010)

Colloquium Mathematicae

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Let d be a positive integer and μ a generalized Cantor measure satisfying μ = j = 1 m a j μ S j - 1 , where 0 < a j < 1 , j = 1 m a j = 1 , S j = ρ R + b j with 0 < ρ < 1 and R an orthogonal transformation of d . Then ⎧1 < p ≤ 2 ⇒ ⎨ s u p r > 0 r d ( 1 / α ' - 1 / p ' ) ( J x r | μ ̂ ( y ) | p ' d y ) 1 / p ' D ρ - d / α ' , x d , ⎩ p = 2 ⇒ infr≥1 rd(1/α’-1/2) (∫J₀r|μ̂(y)|² dy)1/2 ≥ D₂ρd/α’ , where J x r = i = 1 d ( x i - r / 2 , x i + r / 2 ) , α’ is defined by ρ d / α ' = ( j = 1 m a j p ) 1 / p and the constants D₁ and D₂ depend only on d and p.

A compactness result in thin-film micromagnetics and the optimality of the Néel wall

Radu Ignat, Felix Otto (2008)

Journal of the European Mathematical Society

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In this paper, we study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem for S 1 -valued maps m ' (the magnetization) of two variables x ' : E ε ( m ' ) = ε | ' · m ' | 2 d x ' + 1 2 | ' | - 1 / 2 ' · m ' 2 d x ' . We are interested in the behavior of minimizers as ε 0 . They are expected to be S 1 -valued maps m ' of vanishing distributional divergence ' · m ' = 0 , so that appropriate boundary conditions enforce line discontinuities. For finite ε > 0 , these line discontinuities are approximated by smooth transition layers, the so-called Néel...

The classical subspaces of the projective tensor products of p and C(α) spaces, α < ω₁

Elói Medina Galego, Christian Samuel (2013)

Studia Mathematica

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We completely determine the q and C(K) spaces which are isomorphic to a subspace of p ̂ π C ( α ) , the projective tensor product of the classical p space, 1 ≤ p < ∞, and the space C(α) of all scalar valued continuous functions defined on the interval of ordinal numbers [1,α], α < ω₁. In order to do this, we extend a result of A. Tong concerning diagonal block matrices representing operators from p to ℓ₁, 1 ≤ p < ∞. The first main theorem is an extension of a result of E. Oja and states...

The ideal of p-compact operators: a tensor product approach

Daniel Galicer, Silvia Lassalle, Pablo Turco (2012)

Studia Mathematica

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We study the space of p-compact operators, p , using the theory of tensor norms and operator ideals. We prove that p is associated to / d p , the left injective associate of the Chevet-Saphar tensor norm d p (which is equal to g p ' ' ). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that p ( E ; F ) is equal to q ( E ; F ) for a wide range of values of p and q, and show that our results...

Elementary operators on Banach algebras and Fourier transform

Miloš Arsenović, Dragoljub Kečkić (2006)

Studia Mathematica

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We consider elementary operators x j = 1 n a j x b j , acting on a unital Banach algebra, where a j and b j are separately commuting families of generalized scalar elements. We give an ascent estimate and a lower bound estimate for such an operator. Additionally, we give a weak variant of the Fuglede-Putnam theorem for an elementary operator with strongly commuting families a j and b j , i.e. a j = a j ' + i a j ' ' ( b j = b j ' + i b j ' ' ), where all a j ' and a j ' ' ( b j ' and b j ' ' ) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class...

Linear natural operators lifting p -vectors to tensors of type ( q , 0 ) on Weil bundles

Jacek Dębecki (2016)

Czechoslovak Mathematical Journal

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We give a classification of all linear natural operators transforming p -vectors (i.e., skew-symmetric tensor fields of type ( p , 0 ) ) on n -dimensional manifolds M to tensor fields of type ( q , 0 ) on T A M , where T A is a Weil bundle, under the condition that p 1 , n p and n q . The main result of the paper states that, roughly speaking, each linear natural operator lifting p -vectors to tensor fields of type ( q , 0 ) on T A is a sum of operators obtained by permuting the indices of the tensor products of linear natural...

Primefree shifted Lucas sequences

Lenny Jones (2015)

Acta Arithmetica

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We say a sequence = ( s ) n 0 is primefree if |sₙ| is not prime for all n ≥ 0, and to rule out trivial situations, we require that no single prime divides all terms of . In this article, we focus on the particular Lucas sequences of the first kind, a = ( u ) n 0 , defined by u₀ = 0, u₁ = 1, and uₙ = aun-1 + un-2 for n≥2, where a is a fixed integer. More precisely, we show that for any integer a, there exist infinitely many integers k such that both of the shifted sequences a ± k are simultaneously primefree. This...

E 1 -degeneration and d ' d ' ' -lemma

Tai-Wei Chen, Chung-I Ho, Jyh-Haur Teh (2016)

Commentationes Mathematicae Universitatis Carolinae

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For a double complex ( A , d ' , d ' ' ) , we show that if it satisfies the d ' d ' ' -lemma and the spectral sequence { E r p , q } induced by A does not degenerate at E 0 , then it degenerates at E 1 . We apply this result to prove the degeneration at E 1 of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of d ' d ' ' -lemma.

Kernel theorems in spaces of generalized functions

Antoine Delcroix (2010)

Banach Center Publications

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In analogy to the classical isomorphism between ((ℝⁿ), ' ( m ) ) and ' ( m + n ) (resp. ( ( ) , ' ( m ) ) and ' ( m + n ) ), we show that a large class of moderate linear mappings acting between the space C ( ) of compactly supported generalized functions and (ℝⁿ) of generalized functions (resp. the space ( ) of Colombeau rapidly decreasing generalized functions and the space τ ( ) of temperate ones) admits generalized integral representations, with kernels belonging to specific regular subspaces of ( m + n ) (resp. τ ( m + n ) ). The main novelty is to use...

Convolution theorems for starlike and convex functions in the unit disc

M. Anbudurai, R. Parvatham, S. Ponnusamy, V. Singh (2004)

Annales Polonici Mathematici

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Let A denote the space of all analytic functions in the unit disc Δ with the normalization f(0) = f’(0) − 1 = 0. For β < 1, let P β = f A : R e f ' ( z ) > β , z Δ . For λ > 0, suppose that denotes any one of the following classes of functions: M 1 , λ ( 1 ) = f : R e z ( z f ' ( z ) ) ' ' > - λ , z Δ , M 1 , λ ( 2 ) = f : R e z ( z ² f ' ' ( z ) ) ' ' > - λ , z Δ , M 1 , λ ( 3 ) = f : R e 1 / 2 ( z ( z ² f ' ( z ) ) ' ' ) ' - 1 > - λ , z Δ . The main purpose of this paper is to find conditions on λ and γ so that each f ∈ is in γ or γ , γ ∈ [0,1/2]. Here γ and γ respectively denote the class of all starlike functions of order γ and the class of all convex functions of order γ. As a consequence, we obtain...

On a system of equations with primes

Paolo Leonetti, Salvatore Tringali (2014)

Journal de Théorie des Nombres de Bordeaux

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Given an integer n 3 , let u 1 , ... , u n be pairwise coprime integers 2 , 𝒟 a family of nonempty proper subsets of { 1 , ... , n } with “enough” elements, and ε a function 𝒟 { ± 1 } . Does there exist at least one prime q such that q divides i I u i - ε ( I ) for some I 𝒟 , but it does not divide u 1 u n ? We answer this question in the positive when the u i are prime powers and ε and 𝒟 are subjected to certain restrictions. We use the result to prove that, if ε 0 { ± 1 } and A is a set of three or more primes that contains all prime divisors of any...

Comaximal graph of C ( X )

Mehdi Badie (2016)

Commentationes Mathematicae Universitatis Carolinae

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In this article we study the comaximal graph Γ 2 ' C ( X ) of the ring C ( X ) . We have tried to associate the graph properties of Γ 2 ' C ( X ) , the ring properties of C ( X ) and the topological properties of X . Radius, girth, dominating number and clique number of the Γ 2 ' C ( X ) are investigated. We have shown that 2 Rad Γ 2 ' C ( X ) 3 and if | X | > 2 then girth Γ 2 ' C ( X ) = 3 . We give some topological properties of X equivalent to graph properties of Γ 2 ' C ( X ) . Finally we have proved that X is an almost P -space which does not have isolated points if and only if C ( X ) is an almost...