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1.
We present a topological analogue of the classic Kadec Renorming Theorem, as follows. Let be two separable metric topologies on the same set X. We prove that every point in X has an -neighbourhood basis consisting of sets that are -closed if and only if there exists a function φ: X→ℝ that is -lower semi-continuous and such that is the weakest topology on X that contains and that makes φ continuous. An immediate corollary is that the class of almost n-dimensional spaces consists precisely of the graphs of lower semi-continuous functions with at most n-dimensional domains. 相似文献
2.
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
3.
Let G=GL(N,K), K a non-archimedean local field and X be the semisimple affine building of G over K. We construct a projective tower of G-sets with X(0)=X. They are obtained by using a minor modification in Bruhat and Tits original construction (an idea due to P. Schneider). Using the structure of X as an abstract building, we construct a projective tower of simplicial G-complexes such that, for each r, X(r) is canonically a geometrical realization of Xr. In the case N=2, Xr has a natural two-sheeted covering r and we show that the supercuspidal part of the cohomology space is characterized by a nice property.Mathematics Subject Classification (2000): 14R25, 20E42, 20G25, 55U10, 57S25 相似文献
4.
In this article we introduce a notion of `division' for rational functions and then give a criterion for hyponormality of
(f, g are rational functions) in the cases where g divides f. Furthermore we show that we may assume, without loss of generality, that g divides f when we consider the hyponormality of .
Supported in part by a grant from Faculty Research Fund, Sungkyunkwan University, 2004.
Supported in part by a grant (R14-2003-006-01000-0) from the Korea Research Foundation. 相似文献
5.
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
6.
Let B be a (not necessarily irreducible) plane curve in 2. In the present article, we prove that if and only if Moreover, we determine the curve B when and Mathematics Subject Classification (2000): 14R05, 14H50, 14J26 相似文献
7.
Given an automorphic line bundle of weight k on the Drinfeld upper half plane X over a local field K, we construct a GL2(K)-equivariant integral lattice in as a coherent sheaf on the formal model underlying Here is ramified of degree 2. This generalizes a construction of Teitelbaum from the case of even weight k to arbitrary integer weight k. We compute and obtain applications to the de Rham cohomology HdR1( X, SymKk(St)) with coefficients in the k-th symmetric power of the standard representation of SL2(K) (where k0) of projective curves X uniformized by X: namely, we prove the degeneration of a certain reduced Hodge spectral sequence computing HdR1( X, SymKk(St)), we re-prove the Hodge decomposition of HdR1( X, SymKk(St)) and show that the monodromy operator on HdR1( X, SymKk(St)) respects integral de Rham structures and is induced by a universal monodromy operator defined on , i.e. before passing to the -quotient.Mathematics Subject Classification (2000): 11F33, 11F12, 11G09, 11G18I wish to thank Peter Schneider and Jeremy Teitelbaum for generously providing me with some helpful private notes on their own work, and for their interest. I am also grateful to Matthias Strauch for useful discussions on odd weight modular forms. I thank Christophe Breuil for his interest and his insisting on lattices for the entire G-action. Finally I thank the referee for his suggestions concerning the presentation of several technical constructions. 相似文献
8.
Let X be any Banach space and T a bounded operator on X. An extension of the pair (X,T) consists of a Banach space in which X embeds isometrically through an isometry i and a bounded operator on such that When X is separable, it is additionally required that be separable. We say that is a topologically transitive extension of (X, T) when is topologically transitive on , i.e. for every pair of non-empty open subsets of there exists an integer n such that is non-empty. We show that any such pair (X,T) admits a topologically transitive extension , and that when H is a Hilbert space, (H,T) admits a topologically transitive extension where is also a Hilbert space. We show that these extensions are indeed chaotic.Mathematics Subject Classification (2000): 47 A 16 相似文献
9.
Riccardo Ghiloni 《Mathematische Annalen》2006,335(4):751-766
Let R be a real closed field and let X be an affine algebraic variety over R. We say that X is universally map rigid (UMR for short) if, for each irreducible affine algebraic variety Z over R, the set of nonconstant rational maps from Z to X is finite. A bijective map from an affine algebraic variety over R to X is called weak change of the algebraic structure of X if it is regular and φ−1 is a Nash map, which preserves nonsingular points. We prove the following rigidity theorem: every affine algebraic variety
over R is UMR up to a weak change of its algebraic structure. Let us introduce another notion. Let Y be an affine algebraic variety over R. We say that X and Y are algebraically unfriendly if all the rational maps from X to Y and from Y to X are trivial, i.e., Zariski locally constant. From the preceding theorem, we infer that, if dim (X)≥1, then there exists a set of weak changes of the algebraic structure of X such that, for each t,s ∈ R with t≠s, and are algebraically unfriendly. This result implies the following expected fact: For each (nonsingular) affine algebraic variety
X over R of positive dimension, the natural Nash structure of X does not determine the algebraic structure of X. In fact, the moduli space of birationally nonisomorphic (nonsingular) affine algebraic varieties over R, which are Nash isomorphic to X, has the same cardinality of R. This result was already known under the special assumption that R is the field of real numbers and X is compact and nonsingular.
The author is a member of GNSAGA of CNR, partially supported by MURST and European Research Training Network RAAG 2002–2006
(HPRN–CT–00271). 相似文献
10.
S. Thangavelu 《Mathematische Annalen》2006,335(4):879-899
We define an analogue of Poisson transform on the Heisenberg group and use it to characterise joint eigenfunctions of the
sublaplacian and T=i∂t in terms of certain analytic functionals. 相似文献
11.
Carolina Araujo 《Mathematische Annalen》2006,335(4):937-951
In this paper we investigate complex uniruled varieties X whose rational curves of minimal degree satisfy a special property. Namely, we assume that the tangent directions to such
curves at a general point x ∈ X form a linear subspace of TxX. As a first application of our main result, we give a unified geometric proof of Mori's, Wahl's, Campana-Peternell's and
Andreatta-Wiśniewski's characterizations of . We also give a characterization of products of projective spaces in terms of the geometry of their families of rational
curves of minimal degree. 相似文献
12.
Let V be a p-adic representation of the absolute Galois group G of that becomes crystalline over a finite tame extension, and assume p2. We provide necessary and sufficient conditions for V to be isomorphic to the p-adic Tate module Vp() of an abelian variety defined over . These conditions are stated on the filtered (,G)-module attached to V.Mathematics Subject Classification (2000): 14F30, 11G10, 11F80, 14G20, 14F20 相似文献
13.
Let be a C*-algebra, a subalgebra of its center and Φ: → a tracial faithful conditional expectation. We define the positive projective space as the quotient
where G+ is the space of positive invertible elements of , and if there exists g invertible in such that a′ = |g|2a. When is abelian, this space is a set of representatives for probability densities equivalent to a given one. The aim of this paper
is to endow ℙ+ with differentiable structure, a linear connection and a Finsler metric. This is done in a way that given any pair of elements
in ℙ+, there is a unique geodesic of this connection, which is the shortest curve joining such endpoints for the given metric.
The metric space ℙ+ with the given geodesic distance is non positively curved. 相似文献
14.
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
15.
Shu Kawaguchi 《Mathematische Annalen》2006,335(2):285-310
Let be a polynomial automorphism of dynamical degree δ≥2 over a number field K. We construct height functions defined on that transform well relative to f, which we call canonical height functions for f. These functions satisfy the Northcott finiteness property, and a -valued point on is f-periodic if and only if its height is zero. As an application, we give an estimate on the number of points with bounded height
in an infinite f-orbit. 相似文献
16.
Given countable directed graphs G and G, we show that the associated tensor algebras (G) and (G) are isomorphic as Banach algebras if and only if the graphs G are G are isomorphic. For tensor algebras associated with graphs having no sinks or no sources, the graph forms an invariant for algebraic isomorphisms. We also show that given countable directed graphs G, G, the free semigroupoid algebras and are isomorphic as dual algebras if and only if the graphs G are G are isomorphic. In particular, spatially isomorphic free semigroupoid algebras are unitarily isomorphic. For free semigroupoid algebras associated with locally finite directed graphs with no sinks, the graph forms an invariant for algebraic isomorphisms as well.Mathematics Subject Classification (2000): 47L80, 47L55, 47L40Acknowledgments. We would like to thank the referee for several constructive suggestions on the initial draft and for bringing to our attention the work in [8,9]. The first author was partially supported by a research grant from ECU and the second author by an NSERC research grant and start up funds from the University of Guelph. We thank David Pitts for enlightening conversations and Alex Kumjian for helpful comments on the literature. 相似文献
17.
We prove that the mean value of the real parts of the nontrivial zeros of the Epstein zeta-function associated with a positive definite quadratic form in n variables is equal to . Furthermore, we show that Epstein zeta-functions in general have an asymmetric zero-distribution with respect to the critical
line Re . 相似文献
18.
Ning Ju 《Mathematische Annalen》2006,334(3):627-642
The two dimensional quasi-geostrophic (2D QG) equation with critical and super-critical dissipation is studied in Sobolev space Hs(ℝ2). For critical case (α=), existence of global (large) solutions in Hs is proved for s≥ when is small. This generalizes and improves the results of Constantin, D. Cordoba and Wu [4] for s = 1, 2 and the result of A. Cordoba and D. Cordoba [8] for s=. For s≥1, these solutions are also unique. The improvement for pushing s down from 1 to is somewhat surprising and unexpected. For super-critical case (α ∈ (0,)), existence and uniqueness of global (large) solution in Hs is proved when the product is small for suitable s≥2−2α, p ∈ [1,∞] and β ∈ (0,1]. 相似文献
19.
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
20.
Andrei Teleman 《Mathematische Annalen》2006,335(4):965-989
We describe the positive cone and the pseudo-effective cone of a non-Kählerian surface. We use these results for two types of applications: 1. Describe the set of possible total Ricci scalars associated with Gauduchon metrics of fixed volume 1 on a fixed non-Kählerian surface, and decide whether the assignment is a deformation invariant. 2. Study the stability of the canonical extension of a class VII surface X with positive b 2. This extension plays an important role in our strategy to prove existence of curves on class VII surfaces, using gauge theoretical methods [Te2]. Our main tools are Buchdahl ampleness criterion for non-Kählerian surfaces [Bu2] and the recent results of Dloussky-Oeljeklaus-Toma [DOT] and Dloussky [D] on class VII surfaces with curves. 相似文献