共查询到20条相似文献,搜索用时 46 毫秒
1.
Laurent Bartholdi 《Israel Journal of Mathematics》2006,154(1):93-139
We develop the theory of “branch algebras”, which are infinite-dimensional associative algebras that are isomorphic, up to
taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees.
In particular, for every field
% MathType!End!2!1! we contruct a
% MathType!End!2!1! which
The author acknowledges support from TU Graz and UC Berkeley, where part of this research was conducted. 相似文献
– | • is finitely generated and infinite-dimensional, but has only finitedimensional quotients; |
– | • has a subalgebra of finite codimension, isomorphic toM 2(k); |
– | • is prime; |
– | • has quadratic growth, and therefore Gelfand-Kirillov dimension 2; |
– | • is recursively presented; |
– | • satisfies no identity; |
– | • contains a transcendental, invertible element; |
– | • is semiprimitive if % MathType!End!2!1! has characteristic ≠2; |
– | • is graded if % MathType!End!2!1! has characteristic 2; |
– | • is primitive if % MathType!End!2!1! is a non-algebraic extension of % MathType!End!2!1!; |
– | • is graded nil and Jacobson radical if % MathType!End!2!1! is an algebraic extension of % MathType!End!2!1!. |
2.
Let X be a Banach space and let (ξj)j ≧ 1 be an i.i.d. sequence of symmetric random variables with finite moments of all orders. We prove that the following assertions
are equivalent:
Received: 10 January 2005; revised: 5 April 2005 相似文献
1. |
There exists a constant K such that
|
|
2. | X is isomorphic to a Hilbert space. |
3.
We introduce a notion which is intermediate between that of taking thew*-closed convex hull of a set and taking the norm closed convex hull of this set. This notion helps to streamline the proof
(given in [FLP]) of the famous result of James in the separable case. More importantly, it leads to stronger results in the
same direction. For example:
相似文献
1. | AssumeX is separable and non-reflexive and its unit sphere is covered by a sequence of balls of radiusa<1. Then for every sequence of positive numbers tending to 0 there is anf εX*, such that ‖f‖ = 1 andf (x)≤1 −ε i , wheneverx εC i ,i=1,2,… |
2. | AssumeX is separable and non-reflexive and letT:Y →X* be a bounded linear non-surjective operator. Then there is anf εX* which does not attain its norm onB X such thatf ∉T(Y). |
4.
An elementw in the free group onr letters defines a mapf
w,G:Gv→G for each groupG. In this note, we show that wheneverw≠1 andG is a semisimple algebraic group,f
w,G is dominant. As an application, we show that for fixedw and Γ
i
a sequence of pairwise non-isomorphic finite simple groups,
.
Partially supported by NSFGrant DMS-0100537. 相似文献
5.
Choonkil BAAK 《数学学报(英文版)》2006,22(6):1789-1796
Let X, Y be vector spaces. It is shown that if a mapping f : X → Y satisfies f((x+y)/2+z)+f((x-y)/2+z=f(x)+2f(z),(0.1) f((x+y)/2+z)-f((x-y)/2+z)f(y),(0.2) or 2f((x+y)/2+x)=f(x)+f(y)+2f(z)(0.3)for all x, y, z ∈ X, then the mapping f : X →Y is Cauchy additive.
Furthermore, we prove the Cauchy-Rassias stability of the functional equations (0.1), (0.2) and (0.3) in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebras. 相似文献
6.
Let X be a compact metric space and let Lip(X) be the Banach algebra of all scalar- valued Lipschitz functions on X, endowed with a natural norm. For each f ∈ Lip(X), σπ(f) denotes the peripheral spectrum of f. We state that any map Φ from Lip(X) onto Lip(Y) which preserves multiplicatively the peripheral spectrum:
σπ(Φ(f)Φ(g)) = σπ(fg), A↓f, g ∈ Lip(X)
is a weighted composition operator of the form Φ(f) = τ· (f °φ) for all f ∈ Lip(X), where τ : Y → {-1, 1} is a Lipschitz function and φ : Y→ X is a Lipschitz homeomorphism. As a consequence of this result, any multiplicatively spectrum-preserving surjective map between Lip(X)-algebras is of the form above. 相似文献
σπ(Φ(f)Φ(g)) = σπ(fg), A↓f, g ∈ Lip(X)
is a weighted composition operator of the form Φ(f) = τ· (f °φ) for all f ∈ Lip(X), where τ : Y → {-1, 1} is a Lipschitz function and φ : Y→ X is a Lipschitz homeomorphism. As a consequence of this result, any multiplicatively spectrum-preserving surjective map between Lip(X)-algebras is of the form above. 相似文献
7.
In a recent paper, Ghenciu and Lewis studied strong Dunford-Pettis sets and made the following two assertions:
While the statements are correct, the proofs are flawed. The difficulty with the proofs is discussed, and a fundamental result
of Elton is used to establish a simple lemma which leads to quick proofs of both (1) and (2).
The online version of the original article can be found at . 相似文献
(1) | The Banach space X * contains a nonrelatively compact strong Dunford-Pettis set if and only if ℓ∞ ↪ X *. |
(2) | If c 0 ↪ Y and H is a complemented subspace of X so that H * is a strong Dunford-Pettis space, then W(X, Y) is not complemented in L(X, Y). |
8.
9.
Belmesnaoui Aqzzouz 《Rendiconti del Circolo Matematico di Palermo》2006,55(2):147-162
We show that if (K,L) is a semi-abelian category, there exists an abelian categoryK
x with the followings properties:
相似文献
1 | The categoryK is a full subcategory ofK x. |
2 | The free objects ofK are projectives inK x. |
3 | A sequence ofK-morphismes isK-exact if, and only if, it isK x-exact. |
4 | To each objectU ofK x we can associate a surjections:X→U whereX is an object ofK. |
10.
In this paper, we show the equivalence of somequasi-random properties for sparse graphs, that is, graphsG with edge densityp=|E(G)|/(
2
n
)=o(1), whereo(1)→0 asn=|V(G)|→∞. Our main result (Theorem 16) is the following embedding result. For a graphJ, writeN
J(x) for the neighborhood of the vertexx inJ, and letδ(J) andΔ(J) be the minimum and the maximum degree inJ. LetH be atriangle-free graph and setd
H=max{δ(J):J⊆H}. Moreover, putD
H=min{2d
H,Δ(H)}. LetC>1 be a fixed constant and supposep=p(n)≫n
−1
D
H. We show that ifG is such that
Moreover, we discuss a setting under which an arbitrary graphH (not necessarily triangle-free) can be embedded inG. We also present an embedding result for directed graphs.
Research supported by a CNPq/NSF cooperative grant.
Partially supported by MCT/CNPq through ProNEx Programme (Proc. CNPq 664107/1997-4) and by CNPq (Proc. 300334/93-1 and 468516/2000-0).
Partially supported by NSF Grant 0071261.
Supported by NSF grant CCR-9820931. 相似文献
(i) | deg G (x)≤C pn for allx∈V(G), | ||
(ii) |
for all 2≤r≤D
H and for all distinct verticesx
1, ...,x
r ∈V(G), |
||
(iii) |
for all but at mosto(n
2) pairs {x
1,x
2} ⊆V(G), |
11.
Let G be a 2-edge-connected simple graph with girth g, independence number α(G), and if one of the following two conditions holds
then G is upper embeddable and the lower bound v − 3g + 7 is best possible. Similarly the result for 3-edge-connected simple graph with girth g and independence number α(G) is also obtained.
Huang Yuanqiu: Partially supported by National Science Foundation of China (No. 10771062) and Program for New Century Excellent
Talents in University (No. NCET-07-0276). 相似文献
(1) | α(G) ≤ 2; | |
(2) | α(G) ≥ 3, and for any three nonadjacent vertices v
i
(i = 1,2,3), it has
|
12.
Nikita A. Karpenko 《manuscripta mathematica》1995,88(1):109-117
We compute degrees of algebraic cycles on certain Severi-Brauer varieties and apply it to show that:
This article was processed by the author using the LATEX style filecljour 1 from Springer-Verlag 相似文献
– | - a generic division algebra of indexp α and exponentp is not decomposable (in a tensor product of two algebras) for any primep and any α except the case whenp=2 and 2 | α; |
– | - the 2-codimensional Chow group CH2 of the Severi-Brauer variety corresponding to the generic division algebra of index 8 and exponent 2 has a non-trivial torsion. |
13.
A. I. Pavlov 《Mathematical Notes》2000,68(3):370-377
The main result of this paper is the following theorem. Suppose thatτ(n) = ∑
d|n
l and the arithmetical functionF satisfies the following conditions:
Then there exist constantsA
1,A
2, andA
3 such that for any fixed \g3\s>0 the following relation holds:
. Moreover, if for any primep the inequality \vbf(p)\vb\s<1 holds and the functionF is strongly multiplicative, thenA
1\s>0.
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 429–438, September, 2000. 相似文献
1) | the functionF is multiplicative; |
2) | ifF(n) = ∑ d|n f(d), then there exists an α>0 such that the relationf(n)=O(n −α) holds asn→∞. |
14.
In a recent paper, Ghenciu and Lewis studied strong Dunford-Pettis sets and made the following two assertions:
While the statements are correct, the proofs are flawed. The difficulty with the proofs is discussed, and a fundamental result
of Elton is used to establish a simple lemma which leads to quick proofs of both (1) and (2). 相似文献
(1) | The Banach space X * contains a nonrelatively compact strong Dunford-Pettis set if and only if ℓ∞ ↪ X *. |
(2) | If c 0 ↪ Y and H is a complemented subspace of X so that H * is a strong Dunford-Pettis space, then W(X, Y) is not complemented in L(X, Y). |
15.
We are going to discuss special cases of a conditional functional inequality
whereX is a real inner product space. In particular, we will give conditions which force the representationf(x)=c‖x‖2+a(x) for x ∈X, where c ∈ R anda:x→ℝ is an additive functional. 相似文献
16.
Kenley Jung 《Mathematische Annalen》2007,338(1):241-248
Suppose M is a tracial von Neumann algebra embeddable into (the ultraproduct of the hyperfinite II1-factor) and X is an n-tuple of selfadjoint generators for M. Denote by Γ(X; m, k, γ) the microstate space of X of order (m, k ,γ). We say that X is tubular if for any ε > 0 there exist and γ > 0 such that if then there exists a k × k unitary u satisfying for each 1 ≤ i ≤ n. We show that the following conditions are equivalent:
Research supported in part by the NSF.
Dedicated to Ed Effros on the occasion of his 70th birthday. 相似文献
• | M is amenable (i.e., injective). |
• | X is tubular. |
• | Any two embeddings of M into are conjugate by a unitary . |
17.
M. Rovinsky 《Selecta Mathematica, New Series》2009,15(2):343-376
Let G be the automorphism group of an extension of algebraically closed fields of characteristic zero of transcendence degree n, 1 ≤ n ≤ ∞. In this paper we
The study of open subgroups is motivated by the study of (the stabilizers of) smooth representations undertaken in [R1, R3].
The functor Γ is an analogue of the global sections functor on the category of sheaves on a smooth proper algebraic variety.
Another result is that ‘interesting’ semilinear representations are ‘globally generated’.
相似文献
• | construct some maximal closed non-open subgroups Gv, and some (all, in the case of countable transcendence degree) maximal open proper subgroups of G; |
• | describe, in the case of countable transcendence degree, the automorphism subgroups over the intermediate subfields (a question of Krull, [K2, §4, question 3b)]); |
• | construct, in the case n = ∞, a fully faithful subfunctor ( − )v of the forgetful functor from the category of smooth representations of G to the category of smooth representations of Gv; |
• | construct, using the functors ( − )v, a subfunctor Γ of the identity functor on , coincident (via the forgetful functor) with the functor Γ on the category of admissible semilinear representations of G constructed in [R3] in the case n = ∞ and . |
18.
Giuseppe Pellegrino 《Rendiconti del Circolo Matematico di Palermo》1998,47(1):141-168
1. | Letm be the greatest integer such that . ThenPG(3,q) contains complete caps of sizek=(m+1)(q+1)+ω, with ω=0, 1, 2. | |
2. |
PG(3,q),q≥5, contains complete caps of size |
|
3. | InPG(3,q) complete caps different from ovaloids have some external planes. |
19.
Let (G, τ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following:
As an application, a version of the Nikodym boundedness theorem for set functions with values in a class of locally solid
topological groups is established. 相似文献
(1) | If (G, τ) has the A(iii)-property, then its completion is an order-complete locally solid lattice group. |
(2) | If G is order-complete and τ has the Fatou property, then the order intervals of G are τ-complete. |
(3) | If (G, τ) has the Fatou property, then G is order-dense in Ĝ and has the Fatou property. |
(4) | The order-bound topology on any commutative lattice group is the finest locally solid topology on it. |
20.
Eric Schmutz 《Central European Journal of Mathematics》2008,6(3):482-487
It is known that the unit sphere, centered at the origin in ℝ
n
, has a dense set of points with rational coordinates. We give an elementary proof of this fact that includes explicit bounds
on the complexity of the coordinates: for every point ν on the unit sphere in ℝ
n
, and every ν > 0; there is a point r = (r
1; r
2;…;r
n) such that:
One consequence of this result is a relatively simple and quantitative proof of the fact that the rational orthogonal group
O(n;ℚ) is dense in O(n;ℝ) with the topology induced by Frobenius’ matrix norm. Unitary matrices in U(n;ℂ) can likewise be approximated by matrices in U(n;ℚ(i))
相似文献
– | ⊎ ‖r-v‖∞ < ε. |
– | ⊎ r is also a point on the unit sphere; Σ r i 2 = 1. |
– | ⊎ r has rational coordinates; for some integers a i , b i . |
– | ⊎ for all . |