共查询到20条相似文献,搜索用时 31 毫秒
1.
Françoise Lust-Piquard 《Journal of Functional Analysis》2007,244(2):488-503
We prove the little Grothendieck theorem for any 2-convex noncommutative symmetric space. Let M be a von Neumann algebra equipped with a normal faithful semifinite trace τ, and let E be an r.i. space on (0,∞). Let E(M) be the associated symmetric space of measurable operators. Then to any bounded linear map T from E(M) into a Hilbert space H corresponds a positive norm one functional f∈E(2)∗(M) such that
2.
Let E be a Banach lattice and L1(μ, E) be the space of E-valued Bochner integrable functions. Some order properties of L1(μ, E) are given. It is shown that Ls∞(μ, Z(E)) is the ideal centre of L1(μ, E) and it is obtained a Radon-Nikodym type theorem for B -integrable functions.
相似文献
3.
Let k be a field and E(n) be the 2
n+1-dimensional pointed Hopf algebra over k constructed by Beattie, Dăscălescu and Grünenfelder [J. Algebra, 2000, 225: 743–770]. E(n) is a triangular Hopf algebra with a family of triangular structures R
M
parameterized by symmetric matrices M in M
n
(k). In this paper, we study the Azumaya algebras in the braided monoidal category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
and obtain the structure theorems for Azumaya algebras in the category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
, where M is any symmetric n×n matrix over k. 相似文献
4.
L. Saloff-Coste 《Journal of Geometric Analysis》2004,14(4):715-733
Let M =G/H be an irreducible homogeneous compact manifold of dimension n equipped with its canonical Riemannian metric. Let γ be
the lowest nonzero eigenvalue of the Laplace operator. Let μ be the normalized Haar measure and μ
t be the heat diffusion measure, i.e., the law of Brownian motion started at a fixed origin in M. We show that the total variation
distance between μt and μ is not small for t ≪λ
−1 logn.This is sharp, up to a factor of two, in the case of compact irreducible simply connected symmetric spaces. 相似文献
5.
Stephen J. Gardiner 《Journal d'Analyse Mathématique》1996,68(1):95-106
Let Ω be an open set in ℝ
n
andE be a relatively closed subset of Ω. Further, letC
e(E) be the collection of real-valued continuous functions onE which extend continuously to the closure ofE in ℝ
n
. We characterize those pairs (Ω,E) which have the following property: every function inC
e(E) which is harmonic onE
0 can be uniformly approximated onE by functions which are harmonic on Ω and whose restrictions toE belong toC
e(E). 相似文献
6.
Indranil Biswas Amit Hogadi Yogish I. Holla 《Central European Journal of Mathematics》2012,10(4):1300-1305
Let C be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic
zero. For a fixed line bundle L on C, let M
C
(r; L) be the coarse moduli space of semistable vector bundles E over C of rank r with ∧
r
E = L. We show that the Brauer group of any desingularization of M
C
(r; L) is trivial. 相似文献
7.
Vladimir Shpilrain 《Israel Journal of Mathematics》1995,91(1-3):307-316
LetE be a bounded Borel subset of ℝn,n≥2, of positive Lebesgue measure andP
E the corresponding ‘Pompeiu transform”. We prove thatP
E is injective onL
p(ℝn) if 1≤p≤2n/(n-1). We explore the connection between this problem and a Wiener-Tauberian type theorem for theM(n) action onL
q(ℝn) for various values ofq. We also take up the question of whenP
E is injective in caseE is of finite, positive measure, but is not necessarily a bounded set. Finally, we briefly look at these questions in the
contexts of symmetric spaces of compact and non-compact type. 相似文献
8.
Walter Parry 《Israel Journal of Mathematics》1992,77(3):265-271
The following theorem is proven. LetM be a closed, orientable, irreducible 3-manifold such that rankH
1(M, ℤ/pℤ)≥3 for some primep. Then either π1(M) is virtually solvable or it contains a free group of rank 2. 相似文献
9.
Let Γ ⊂ ℝn, n ≥ 2, be the boundary of a bounded domain. We prove that the translates by elements of Γ of functions which transform according
to a fixed irreducible representation of the orthogonal group form a dense class in L
p
(ℝn) for
. A similar problem for noncompact symmetric spaces of rank one is also considered. We also study the connection of the above
problem with the injectivity sets for weighted spherical mean operators.
The first author was supported in part by a grant from UGC via DSA-SAP Phase IV. 相似文献
10.
Alexander Brudnyi 《Arkiv f?r Matematik》2004,42(1):31-59
LetM be a non-compact connected Riemann surface of a finite type, andR⋐M be a relatively compact domain such thatH
1(M,Z)=H
1(R,Z). Let
be a covering. We study the algebraH
∞(U) of bounded holomorphic functions defined in certain subdomains
. Our main result is a Forelli type theorem on projections inH
∞(D).
Research supported in part by NSERC. 相似文献
11.
Let G be the circuit graph of any connected matroid M with minimum degree 5(G). It is proved that its connectivity κ(G) ≥2|E(M) - B(M)| - 2. Therefore 5(G) ≥ 2|E(M) - B(M)| - 2 and this bound is the best possible in some sense. 相似文献
12.
Kazem Khashyarmanesh 《Proceedings Mathematical Sciences》2010,120(1):35-43
Let (R, m) be a commutative Noetherian local ring with non-zero identity, a a proper ideal of R and M a finitely generated R-module with aM ≠ M. Let D(−) ≔ Hom
R
(−, E) be the Matlis dual functor, where E ≔ E(R/m) is the injective hull of the residue field R/m. In this paper, by using a complex which involves modules of generalized fractions, we show that, if x
1, …, x
n
is a regular sequence on M contained in α, then H
(x1, …,xnR
n
D(H
a
n
(M))) is a homomorphic image of D(M), where H
b
i
(−) is the i-th local cohomology functor with respect to an ideal b of R. By applying this result, we study some conditions on a certain module of generalized fractions under which D(H
(x1, …,xn)R
n
(D(H
a
n
(M)))) ⋟ D(D(M)). 相似文献
13.
Let M^n be an n-dimensional complete noncompact oriented weakly stable constant mean curvature hypersurface in an (n + 1)-dimensional Riemannian manifold N^n+1 whose (n - 1)th Ricci curvature satisfying Ric^N(n-1) (n - 1)c. Denote by H and φ the mean curvature and the trace-free second fundamental form of M respectively. If |φ|^2 - (n- 2)√n(n- 1)|H||φ|+ n(2n - 1)(H^2+ c) 〉 0, then M does not admit nonconstant bounded harmonic functions with finite Dirichlet integral. In particular, if N has bounded geometry and c + H^2 〉 0, then M must have only one end. 相似文献
14.
Let N be a restriction of a 3-connected matroid M and let M
′ be a 3-connected minor of M that is minimal having N as a restriction. This paper gives a best-possible upper bound on |E(M
′)−E(N)|.
Received: July 17, 1998 Revised: March 15, 1999 相似文献
15.
Let R be a noetherian ring,
\mathfraka{\mathfrak{a}} an ideal of R, and M an R-module. We prove that for a finite module M, if
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is minimax for all i ≥ r ≥ 1, then
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is artinian for i ≥ r. A local–global principle for minimax local cohomology modules is shown. If
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is coatomic for i ≤ r (M finite) then
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is finite for i ≤ r. We give conditions for a module which is locally minimax to be a minimax module. A non-vanishing theorem and some vanishing
theorems are proved for local cohomology modules. 相似文献
16.
Reza Sazeedeh 《Proceedings Mathematical Sciences》2007,117(4):429-441
Let M be a finitely generated graded module over a Noetherian homogeneous ring R with local base ring (R
0, m0). If R
0 is of dimension one, then we show that reg
i+1(M) and coreg
i+1(M) are bounded for all i ∈ ℕ0. We improve these bounds, if in addition, R
0 is either regular or analytically irreducible of unequal characteristic. 相似文献
17.
Let B be an unbounded domain located outside an angle domain with vertex at the origin, A ={λn}(n = 1,2,...) be a sequence of complex numbers satisfying sup | arg(λn)| 〈 α 〈 π/2 and denote by M(∧) = {z^λ, λ ∈ ∧} the corresponding system of functions z^λ(λ∈∧). Let α0(z) be a weight function defined on B. We obtain a completeness theorem for the system M(∧) in the Hilbert space L^2 [B, α0]. 相似文献
18.
We give an estimate of the smallest spectral value of the Laplace operator on a complete noncompact stable minimal hypersurface
M in a complete simply connected Riemannian manifold with pinched negative sectional curvature. In the same ambient space,
we prove that if a complete minimal hypersurface M has sufficiently small total scalar curvature then M has only one end. We also obtain a vanishing theorem for L
2 harmonic 1-forms on minimal hypersurfaces in a Riemannian manifold with sectional curvature bounded below by a negative constant.
Moreover, we provide sufficient conditions for a minimal hypersurface in a Riemannian manifold with nonpositive sectional
curvature to be stable. 相似文献
19.
Nicole Tomczak-Jaegermann 《Israel Journal of Mathematics》1983,46(1-2):40-66
We show that the Banach-Mazur distance betweenN-dimensional symmetric spacesE andF satisfies
, wherec is a numerical constant. IfE is a symmetric space, then
max (M
(2)(E),M
(2)(E)), whereM
(2)(E) (resp.M
(2)(E)) denotes the 2-convexity (resp. the 2-concavity) constant ofE. We also give an example of a spaceF with an 1-unconditional basis and enough symmetries that satisfiesd(F, l
2
dimF
)=M
(2)(F)M
(2)(F).
Partially supported by NSF Grant MCS-8201044. 相似文献
20.
Brian Curtin 《Graphs and Combinatorics》1999,15(2):143-158
Let Γ=(X,E) denote a bipartite distance-regular graph with diameter D≥4, and fix a vertex x of Γ. The Terwilliger algebra
T=T(x) is the subalgebra of Mat
X(C) generated by A, E
*
0, E
*
1,…,E
*
D, where A denotes the adjacency matrix for Γ and E
*
i denotes the projection onto the i
TH subconstituent of Γ with respect to x. An irreducible T-module W is said to be thin whenever dimE
*
i
W≤1 for 0≤i≤Di. The endpoint of W is min{i|E
*
i
W≠0}.
We determine the structure of the (unique) irreducible T-module of endpoint 0 in terms of the intersection numbers of Γ. We show that up to isomorphism there is a unique irreducible
T-module of endpoint 1 and it is thin. We determine its structure in terms of the intersection numbers of Γ. We determine the
structure of each thin irreducible T-module W of endpoint 2 in terms of the intersection numbers of Γ and an additional real parameter ψ=ψ(W), which we refer to as the type of W.
We now assume each irreducible T-module of endpoint 2 is thin and obtain the following two-fold result. First, we show that the intersection numbers of Γ
are determined by the diameter D of Γ and the set of ordered pairs
where Φ2 denotes the set of distinct types of irreducible T-modules with endpoint 2, and where mult(ψ) denotes the multiplicity with which the module of type ψ appears in the standard
module. Secondly, we show that the set of ordered pairs {(ψ,mult(ψ)) |ψ∈Φ2} is determined by the intersection numbers k, b
2, b
3 of Γ and the spectrum of the graph , where
and where ∂ denotes the distance function in Γ. Combining the above two results, we conclude that if every irreducible T-module of endpoint 2 is thin, then the intersection numbers of Γ are determined by the diameter D of Γ, the intersection numbers k, b
2, b
3 of Γ, and the spectrum of Γ2
2.
Received: November 13, 1995 / Revised: March 31, 1997 相似文献