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1.
Juan Antonio López Molina 《Positivity》2007,11(1):95-117
We study an (n + 1)-tensor norm generalizing Saphar’s classic norm to (n+1)-fold tensor products.We characterize the maps in the minimal and maximal multilinear operator ideals related to in the sense of Defant and Floret.
Partially supported by the MEC and FEDER project MTM2004-02262 and AVCIT group 03/050. 相似文献
2.
We prove Lp-spectral independence for generators of C0-semigroups estimated by the positive C0-semigroup . In the preliminary process of the proof, we obtain the asymptotic expansion formula for the integral kernel of the C0-semigroup . 相似文献
3.
Seyed Mahmoud Manjegani 《Positivity》2007,11(2):239-250
If A1, . . . , Am are positive semidefinite n × n matrices, and if p1, . . . , pm are positive real numbers such that then
where |X| denotes and tr(X) denotes the trace of X. Moreover, equality holds in either of these inequalities if and only if . This result will be shown to hold as well in unital C*-algebras that have a faithful tracial state. 相似文献
4.
The aim of this paper is to prove some stability result for nonlinear elliptic systems of the form
where Δp denotes the p-Laplacian operator defined by Δpz = div(|∇ z|p-2∇ z); p > 2, Ω is a bounded domain in RN (N > 1) with smooth boundary where with h = 1 when α = 1, λ is a positive parameter and f,g are C2 functin on [0,∞) × [0,∞). We prove stability and instability results of positive stationary solutions under various choices
of f and g. 相似文献
5.
If E and F are real Banach lattices and there is an algebra and order isomorphism Φ:(E) →(F) between their respective ordered Banach algebras of regular operators then there is a linear order isomorphism U:E→F such that Φ(T) =UTU−1 for all T ∈ (E). 相似文献
6.
Mohamed Ali Toumi 《Positivity》2007,11(2):357-368
Let A be an Archimedean vector lattice, let be its Dedekind completion and let B be a Dedekind complete vector lattice. If Ψ 0:A × A→ B is a positive orthosymmetric bimorphism, then there exists a positive bimorphism extension Ψ of Ψ 0 to × in B which is orthosymmetric. This leads to a new and short proof of the commutativity of the almost f-algebras multiplications. 相似文献
7.
Odd Degree Polynomials on Real Banach Spaces 总被引:1,自引:0,他引:1
A classical result of Birch claims that for given k, n integers, n-odd there exists some N = N(k, n) such that for an arbitrary n-homogeneous polynomial P on , there exists a linear subspace of dimension at least k, where the restriction of P is identically zero (we say that Y is a null space for P). Given n > 1 odd, and arbitrary real separable Banach space X (or more generally a space with w*-separable dual X*), we construct an n-homogeneous polynomial P with the property that for every point 0 ≠ x ∈ X there exists some k ∈ such that every null space containing x has dimension at most k. In particular, P has no infinite dimensional null space. For a given n odd and a cardinal τ , we obtain a cardinal N = N(τ, n) = expn+1τ such that every n-homogeneous polynomial on a real Banach space X of density N has a null space of density τ .
Some of the work on this paper was done while the first author was a visitor to the Departamento de Análisis Matemático of
the Universidad Complutense de Madrid, to which great thanks are given. The research of the second author was supported by
grants: Institutional Research Plan AV0Z10190503, A100190502, GA ČR 201/04/0090. 相似文献
8.
Stevo Todorcevic 《Mathematische Annalen》2006,335(3):687-715
We show that every Banach space X of density smaller that the Baire category number admits a quotient with a long Schauder basis that can be taken of length ω1 if X is not separable. So, assuming that the Baire category number does not take its minimal possible value, a Banach space X is separable if and only if all biorthogonal systems of X are countable. 相似文献
9.
Dumitru Popa 《Positivity》2006,10(1):87-94
We introduce in a natural way the notion of measure with bounded variation with respect to a normed ideal of operators and
prove that for each maximal normed ideal of operators (, ), is true the following result: If U ∈ L(C(T,X), Y) with G the representing measure of U and G : Σ → ((X, Y),) has bounded variation, then U ∈ (C(T,X), Y). As an application of this result we prove that an injective tensor product of an integral operator with an operator belonging
to a maximal normed ideal of operators (,) belongs also to (, ). 相似文献
10.
Let be an n-uniform hypergraph on 2n vertices. Suppose that and holds for all F1,F2,F3 ∈ . We prove that the size of is at most .
The second author was supported by MEXT Grant-in-Aid for Scientific Research (B) 16340027 相似文献
11.
Matěj Stehlík 《Graphs and Combinatorics》2006,22(3):421-426
A hypergraph is τ-critical if τ(−{E})<τ() for every edge E ∈ , where τ() denotes the transversal number of . We show that if is a connected τ-critical hypergraph, then −{E} can be partitioned into τ()−1 stars of size at least two, for every edge E ∈ . An immediate corollary is that a connected τ-critical hypergraph has at least 2τ()−1 edges. This extends, in a very natural way, a classical theorem of Gallai on colour-critical graphs, and is equivalent
to a theorem of Füredi on t-stable hypergraphs. We deduce a lower bound on the size of τ-critical hypergraphs of minimum degree at least two. 相似文献
12.
Let L be a σ-complete D-lattice and BV the AL-space of all realvalued, null in zero, functions on L of bounded variation. We prove the existence of a continuous Aumann-Shapley operator on the closed subspace of BV generated by powers of nonatomic σ-additive positive modular measures on L. The integral representation of on a class of functions that correspond to measure games is also exhibited.
Dedicated to Professor Paolo De Lucia on the occasion of his 70th birthday. 相似文献
13.
In this paper, it has been proved that and are factorable, where ⊗ denotes wreath product of graphs. As a consequence, a resolvable (k,n,k,2λ) multipartite –design exists for even k. These results generalize the results of Ushio on –factorizations of complete tripartite graphs. 相似文献
14.
Robbert Beukema 《Positivity》2006,10(1):17-37
A positive operator-valued measure is a (weak-star) countably additive set function from a σ-field Σ to the space of nonnegative
bounded operators on a separable complex Hilbert space . Such functions can be written as M = V*E(·)V in which E
is a spectral measure acting on a complex Hilbert space and V is a bounded operator from to such that the only closed linear subspace of , containing the range of V and reducing E (Σ), is itself. Attention is paid to an existing notion of maximality
for positive operator-valued measures. The purpose of this paper is to show that
M is maximal if and only if E, in the above representation of M, generates a maximal commutative von Neumann algebra. 相似文献
15.
Konrad Schmüdgen 《Mathematische Zeitschrift》2006,254(3):641-653
Let G be a connected and simply connected real Lie group with Lie algebra
. Semialgebraic subsets of the unitary dual of G are defined and a strict Positivstellensatz for positive elements of the universal enveloping algebra
of
is proved.
An erratum to this article is available at . 相似文献
16.
Michael Fraboni 《Mathematische Zeitschrift》2006,254(3):553-566
Let C be a nowhere dense compact analytic subset of a 2-dimensional complex manifold X. A result of Napier is the construction of a neighborhood V of C such that for any covering space
in which
is holomorphically convex, there is a C
∞ exhaustion function φ on
which is strictly plurisubharmonic on π-1(V) away from the compact irreducible components of
. Colţoiu and Vajaitu obtained a q-convex version of this result for C a q-dimensional fiber of a proper surjective submersion X→Y. The goal of this paper is a similar version for Cprojective. 相似文献
17.
Assuming CH, let be the saturated random graph of cardinality 1. In this paper we prove that it is consistent that and can be any two prescribed regular cardinals subject only to the requirement 相似文献
18.
The canonical cone structure on a compact Hermitian symmetric space G/P is the fiber bundle
where
is the cone of the highest weight vectors under the action of the reductive part of P. It is known that the cone
coincides with the cone
of the vectors tangent to the lines in G/P passing through x, when we consider G/P as a projective variety under its homogeneous embedding into the projective space
of the irreducible representation space V
of G with highest weight associated to P. A subvariety X of G/P is said to be an integral variety of
at all smooth points xG/P. Equivalently, an integral variety of
is a subvariety of G/P whose embedded projective tangent space at each smooth point is a linear space
We prove a kind of rigidity of the integral varieties under some dimension condition. After making a uniform setting to study the problem, we apply the theory of Lie algebra cohomology as a main tool. Finally we show that the dimension condition is necessary by constructing counterexamples. 相似文献
19.
Hideyo Sasaki 《manuscripta mathematica》2006,119(1):97-106
Let be a real quadratic field with m a square-free positive rational integer, and be the ring of integers in F. An -lattice L on a totally positive definite quadratic space V over F is called r-universal if L represents all totally positive definite -lattices l with rank r over . We prove that there exists no 2-universal -lattice over F with rank less than 6, and there exists a 2-universal -lattice over F with rank 6 if and only if m=2, 5. Moreover there exists only one 2-universal -lattice with rank 6, up to isometry, over . 相似文献
20.
Jérémy Blanc 《manuscripta mathematica》2006,119(2):225-241
We describe the conjugacy classes of affine automorphisms in the group Aut(n,) (respectively Bir()) of automorphisms (respectively of birational maps) of . From this we deduce also the classification of conjugacy classes of automorphisms of ℙn in the Cremona group Bir(). 相似文献