共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
We relate Artin's braid groupB
℞=lim→Bn to a certain groupF′ ofpl-homeomorphisms of the interval. Namely, there exists a short exact sequence 1→B
∞→A→F′→1 whereH
kA=0,k≥1. 相似文献
3.
N. B. Brodskii 《Mathematical Notes》1999,66(3):283-291
A new method for extending upper semicontinuousUV
n
-valued mappings is introduced. Any upper semicontinuousUV
n
-valued mapping Ψ:A→Y of a closed subsetA of a separable metric spaceX into ann-connected, locallyn-connected complete metric spaceY satisfying the property of disjoint (n+1)-disks is proved to be extendable to an upper semicontinuousUV
n
-valued mapping Ψ′:X→Y such that Ψ′|a=Ψ. As an application, some results aboutn-soft mappings are obtained.
Translated fromMatematicheskie Zametki, Vol. 66, No. 3, pp. 351–363, September, 1999. 相似文献
4.
Let A, B be two archimedean ℓ-algebras and let U,V be two positive linear maps from A to B. We call that the couple (U,V) is separating with respect to A and B if |a||b| = 0 in A implies |U (a)||V (b)| = 0 in B. In this paper, we prove that if A is an f-algebra with unit elment e, if B is an ℓ-algebra and if (U,V) is a separating couple with respect to A and B then (U
∼∼,V
∼∼), where U
∼∼ (resp V
∼∼) is the bi-adjoint of U (resp of V), is again a separating couple with respect to the order continuous order biduals (A′)′
n
and (B′)′
n
of A and B respectively furnished with their Arens products respectively. Moreover, in the case where B′ separates the points of B, we give a characterization of any separating couple with respect to A and B.
相似文献
5.
D. V. Gugnin 《Proceedings of the Steklov Institute of Mathematics》2009,266(1):59-90
We introduce and study polynomially dependent homomorphisms, which are special linear maps between associative algebras with
identity. The multiplicative structure is much involved in the definition of such homomorphisms (we consider only the case
of maps f: A → B with commutative B). The most important particular case of these maps are the Frobenius n-homomorphisms, which were introduced by V.M. Buchstaber and E.G. Rees in 1996–1997. A 1-homomorphism f: A → B is just an algebra homomorphism (the algebra B is commutative). A typical example of an n-homomorphism is given by the sum of n algebra homomorphisms, f = f
1 + ... + f
n
, f
i
: A → B, 1 ≤ i ≤ n. Another example is the trace of n × n matrices over a field R of characteristic zero, tr: M
n
(R) → R, and, more generally, the character of any n-dimensional representation, tr ρ: A → R, ρ: A → M
n
(R). The properties of n-homomorphisms (some of which were proved by Buchstaber and Rees under additional conditions) are derived, and a general theory
of polynomially dependent homomorphisms is developed. One of the main results of the paper is a uniqueness theorem, which
distinguishes the classes of n-homomorphisms among all polynomially dependent homomorphisms by a single natural completeness condition. As a topological
application of n-homomorphisms, we consider the theory of n-homomorphisms between commutative C*-algebras with identity. We prove that the norm of any such n-homomorphism is equal to n and describe the structure of all such n-homomorphisms, which generalizes the classical Gelfand transform (the case of n = 1). An interesting fact discovered is that the Gelfand transform, which is a functorial bijection between appropriate spaces
of maps, becomes a homeomorphism after considering natural topologies on these spaces. 相似文献
6.
Summary LetA→A′ be a regular morphism between two noetherian rings. Then for everyA-algebra of finite typeB, everyA-morphism fromB toA′ can be factorised through aB-algebra of finite typeB′ which is standard (smooth) overA and which is ?as smooth as possible? overB (i.e. except above the singular locus ofB overA). This result is a positive answer to one conjecture due to M. Artin.
Riassunto SiaA→A′ un omomorfismo regolare di anelli noetheriani. Si dimostra che per ogniA-algebraB di tipo finito, ogniA-omomorfismoB→A′ si può fattorizzare mediante unaB-algebraB′ di tipo finito che è liscia suA ed è ?la più liscia posibile? suB (più precisamente liscia suB meno il luogo singolare diB suA). Questo risultato è una risposta affermativa a una congettura di M. Artin.相似文献
7.
In this paper, we consider a triple of Gromov-Hausdorff convergence: $
A_i ^{\underrightarrow {d_{GH} }} A,B_i ^{\underrightarrow {d_{GH} }} A
$
A_i ^{\underrightarrow {d_{GH} }} A,B_i ^{\underrightarrow {d_{GH} }} A
and maps f
i
: A
i
→ B
i
converge to a map f: A → B, where A
i
are compact Alexandrov n-spaces and B
i
are compact Riemannian m-manifolds such that the curvature, diameter and volume are suitably bounded (non-collapsing). When f is a submetry, we give a necessary and sufficient condition for the sequence to be stable, that is, for i large, there are homeomorphisms, Ψ
i
: A
i
→ A, Φ
i
: B
i
→ B such that f ∘ Ψ
i
= Φ
i
∘ f
i
. When f is an ε-submetry with ε > 0, we obtain a sufficient condition for the stability in the case that A
i
are Riemannian manifolds. Our results generalize the stability/finiteness results on fiber bundles by Riemannian submersions
and by submetries. 相似文献
8.
Jouko Tervo 《Israel Journal of Mathematics》1988,63(1):41-66
The paper considers a boundary value problem with the help of the smallest closed extensionL
∼ :H
k →H
k
0×B
h
1×...×B
h
N
of a linear operatorL :C
(0)
∞
(R
+
n
) →L(R
+
n
)×L(R
n−1)×...×L(R
n−1). Here the spacesH
k (the spaces ℬ
h
) are appropriate subspaces ofD′(R
+
n
) (ofD′(R
n−1), resp.),L(R
+
n
) andC
(0)
∞
(R
+
n
)) denotes the linear space of smooth functionsR
n
→C, which are restrictions onR
+
n
of a function from the Schwartz classL (fromC
0
∞
, resp.),L(R
n−1) is the Schwartz class of functionsR
n−1 →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L
∼) and for the uniqueness of solutionsL
∼
U=F are expressed. In addition, ana priori estimate for the corresponding boundary value problem is established. 相似文献
9.
Adrian Constantin 《Annali dell'Universita di Ferrara》1995,41(1):1-4
LetH be a complex Hilbert space and letB be the space of all bounded linear operators fromH intoH with the strong operator topology. We will give a boundedness result for the solutions of the differential equationx′=A(t)x+f(t,x) whereA: I=[t
0, ∞)→B is continuous,f: I×H→H is also continuous and for every bounded setS⊂I×H there exists a constantM(S)>0 such that |f(t,x)−f(t,y)|≤M(S)|x−y|,(t,x), (t,y)∈S.
Sunto SiaH uno spazio di Hilbert complesso e siaB lo spazio degli operatori lineari limitati daH inH, con la topologia forte. In questo lavoro si prova un risultato di limitatezza per le soluzioni dell'equazione differenzialex′=A(t)x+f(t,x), doveA: I=[t 0, ∞)→B è continua,f: I×H→H è continua e per ogni insieme limitatoS⊂I×H esiste una costanteM(S)>0 tale che |f(t,x)−f(t,y)|≤M(S)|x−y| per ogni(t,x), (t,y)∈S.相似文献
10.
Wu Liangsen 《数学学报(英文版)》1992,8(4):406-412
LetA, B be unitalC
*-algebras,D
A
1
the set of all completely positive maps ϕ fromA toM
n
(C), with Tr ϕ(I)≤1(n≥3). If Ψ is an α-invariant affine homeomorphism betweenD
A
1
andD
B
1
with Ψ (0)=0, thenA is*-isomorphic toB.
Obtained results can be viewed as non-commutative Kadison-Shultz theorems.
This work is supported by the National Natural Science Foundation of China. 相似文献
11.
V. M. Prokip 《Ukrainian Mathematical Journal》2012,63(8):1314-1320
Polynomial n × n matrices A(x) and B(x) over a field
\mathbbF \mathbb{F} are called semiscalar equivalent if there exist a nonsingular n × n matrix P over
\mathbbF \mathbb{F} and an invertible n × n matrix Q(x) over
\mathbbF \mathbb{F} [x] such that A(x) = PB(x)Q(x). We give a canonical form with respect to semiscalar equivalence for a matrix pencil A(x) = A
0x
- A
1, where A
0 and A
1 are n × n matrices over
\mathbbF \mathbb{F} , and A
0 is nonsingular. 相似文献
12.
Let B be a domain, Q a maximal ideal of B, π: B → B/Q the canonical surjection, D a subring of B/Q, and A:=π
−1(D). If both B and D are almost-divided domains (resp., n-divided domains), then A = B ×
B/Q
D is an almost-divided domain (resp., an n-divided domain); the converse holds if B is quasilocal. If 2 ≤ d ≤ ∞, an example is given of an almost-divided domain of Krull dimension d which is not a divided domain.
相似文献
13.
This paper deals with the set-valued vector quasiequilibrium problem of finding a point (z
0,x
0) of a set E×K such that (z
0,x
0)∈B(z
0,x
0)×A(z
0,x
0), and, for all η∈A(z
0,x
0),
where α is a subset of 2
Y
×2
Y
and A:E×K→2
K
,B:E×K→2
E
,F:E×K×K→2
Y
, C:E×K×K→2
Y
are set-valued maps, with Y is a topological vector space. Two existence theorems are proven under different assumptions. Correct results of [Hou, S.H.,
Yu, H., Chen, G.Y.: J. Optim. Theory Appl. 119, 485–498 (2003)] are obtained from a special case of one of these theorems.
The authors are indebted to the referees for valuable remarks. 相似文献
14.
C. M. da Fonseca 《Journal of Mathematical Sciences》2006,139(4):6823-6830
Let A and B be (n×n)-matrices. For an index set S ⊂ {1, …, n}, denote by A(S) the principal submatrix that lies in the rows and columns indexed by S. Denote by S′ the complement of S and define η(A, B) =
det A(S) det B(S′), where the summation is over all subsets of {1, …, n} and, by convention, det A(∅) = det B(∅) = 1. C. R. Johnson conjectured that if A and B are Hermitian and A is positive semidefinite, then the polynomial η(λA,-B) has only real roots. G. Rublein and R. B. Bapat proved that this is true for n ⩽ 3. Bapat also proved this result for any n with the condition that both A and B are tridiagonal. In this paper, we generalize some little-known results concerning the characteristic polynomials and adjacency
matrices of trees to matrices whose graph is a given tree and prove the conjecture for any n under the additional assumption that both A and B are matrices whose graph is a tree.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 3, pp. 245–254, 2004. 相似文献
15.
Wolfgang Hackenbroch 《manuscripta mathematica》1990,66(1):351-357
Given two σ-algebrasU ⊂A, invariant under a fixed semigroupG of transformations, the following subsetC of the lattice coneM (U)
G
ofG-invariant finite measures onU is shown to be (the positive part of) a band inM (U)
G
: AG-invariant measure μ belongs toC iff the setexM
Bμ)
G
of extremalG-invariant extensions of μ toB is non-empty and eachG-invariant extensionv of μ admits a barycentric decompositionv=→v′ρ(dv′) with some representing probability ρ onexM
U μ)
G
.—Any band of extensible measures allows to study the corresponding extension problem locally. 相似文献
16.
Christine Lescop 《Inventiones Mathematicae》1998,133(3):613-681
We study the following question: How does the Casson-Walker invariant λ of a rational homology 3-sphere obtained by gluing
two pieces along a surface depend on the two pieces? Our partial answer may be stated as follows. For a compact oriented 3-manifold
A with boundary ∂A, the kernel L
A
of the map from H
1(∂A;Q) to H
1(A;Q) induced by the inclusion is called the Lagrangian of A. Let Σ be a closed oriented surface, and let A, A′, B and B′ be four rational homology handlebodies such that ∂A, ∂A′, −∂B and −∂B′ are identified via orientation-preserving homeomorphisms with Σ. Assume that L
A
= L
A
′ and L
B
= L
B
′ inside H
1(Σ;Q) and also assume that L
A
and L
B
are transverse. Then we express
in terms of the form induced on ∧3 L
A
by the algebraic intersection on H
2(A∪Σ−A′) paired to the analogous form on ∧3 L
B
via the intersection form of Σ. The simple formula that we obtain naturally extends to the extension of the Casson-Walker
invariant of the author. It also extends to gluings along non-connected surfaces.
Oblatum 6-III-1995 & 31-X-1997 相似文献
17.
Ignacio Villanueva 《Monatshefte für Mathematik》2002,137(2):167-172
If K is an uncountable metrizable compact space, we prove a “factorization” result for a wide variety of vector valued Borel measures
μ defined on K
n
. This result essentially says that for every such measure μ there exists a measure μ′ defined on K such that the measure μ of a product A
1 × ⋯ × A
n
of Borel sets of K equals the measure μ′ of the intersection A
1′∩⋯∩A
n
′, where the A
i
′’s are certain transforms of the A
i
’s.
Partially supported by DGICYT grant PB97-0240.
Received August 23, 2001; in revised form March 21, 2002 相似文献
18.
P. H. Sach 《Journal of Optimization Theory and Applications》2008,139(2):337-350
This paper considers the following generalized vector quasiequilibrium problem: find a point (z
0,x
0) of a set E×K such that x
0∈A(z
0,x
0) and
where α is a subset of 2
Y
×2
Y
, A:E×K→2
K
, B:E×K×K→2
E
, C:E×K×K→2
Y
, F:E×K×K→2
Y
are set-valued maps and Y is a topological vector space. Existence theorems are established under suitable assumptions, one of which is the requirement
of the openness of the lower sections of some set-valued maps which can be satisfied with maps B,C, F being discontinuous. It is shown that, in some special cases, this requirement can be verified easily by using the semicontinuity
property of these maps. Another assumption in the obtained existence theorems is assured by appropriate notions of diagonal
quasiconvexity.
The author thanks the referees for valuable comments. 相似文献
19.
G. F. Webb 《Israel Journal of Mathematics》1972,12(3):237-248
It is shown that a strongly continuous semi-group of nonlinear nonexpansive operators can be constructed as lim
n→∞ ((I+t/nB)−1 (I+t/nB)−1)
n
whereA is a linearm-accretive operator,B is a nonlinearm-accretive operator, andB satisfies a boundedness condition relative toA. 相似文献
20.
Let D, D′ ⊂ ℂn be bounded domains with smooth real analytic boundaries and ƒ: D → D′ be a proper holomorphic map. Our main result implies
that if the graph of ƒ extends as an analytic set to a neighborhood of a poìnt (a, a′) ∈ ∂D × 3D′ with a′ ∈ clƒ(a), then ƒ extends holomorphically to a neighborhood of a. 相似文献