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2.
Let L be a J-subspace lattice on a Banach space X and Alg L the associated J-subspace lattice algebra. Let A be a standard operator subalgebra (i.e., it contains all finite rank operators in AlgL) of AlgL and M■B(X) the Alg L-bimodule. It is shown that every linear Jordan triple derivation from A into M is a derivation, and that every generalized Jordan (triple) derivation from A into M is a generalized derivation. 相似文献
3.
4.
The chaos caused by a strong-mixing preserving transformation is discussed and it is shown that for a topological spaceX satisfying the second axiom of countability and for an outer measurem onX satisfying the conditions: (i) every non-empty open set ofX ism-measurable with positivem-measure; (ii) the restriction ofm on Borel σ-algebra ℬ(X) ofX is a probability measure, and (iii) for everyY⊂X there exists a Borel setB⊂ℬ(X) such thatB⊃Y andm(B) =m(Y), iff:X→X is a strong-mixing measure-preserving transformation of the probability space (X, ℬ(X),m), and if {m}, is a strictly increasing sequence of positive integers, then there exists a subsetC⊂X withm (C) = 1, finitely chaotic with respect to the sequence {m
i}, i.e. for any finite subsetA ofC and for any mapF:A→X there is a subsequencer
i such that limi→∞
f
r
i(a) =F(a) for anya ∈A. There are some applications to maps of one dimension.
the National Natural Science Foundation of China. 相似文献
5.
Dmitry Dordovskyi Oleksiy Dovgoshey Eugeniy Petrov 《P-Adic Numbers, Ultrametric Analysis, and Applications》2011,3(4):253-262
Let F(X) be the set of finite nonempty subsets of a set X. We have found the necessary and sufficient conditions under which for a given function τ: F(X) → ℝ there is an ultrametric on X such that τ(A) = diamA for every A ∈ F(X). For finite nondegenerate ultrametric spaces (X, d) it is shown that X together with the subset of diametrical pairs of points of X forms a complete k-partite graph, k ⩾ 2, and, conversely, every finite complete k-partite graph with k ⩾ 2 can be obtained by this way. We use this result to characterize the finite ultrametric spaces (X, d) having the minimal card{(x, y): d(x, y) = diamX, x, y ∈ X} for given card X. 相似文献
6.
Ioan I. Vrabie 《Israel Journal of Mathematics》1979,32(2-3):221-235
LetX be a real Banach space,U ⊂X a given open set,A ⊂X×X am-dissipative set andF:C(0,a;U) →L
∞(0,a;X) a continuous mapping. Assume thatA generates a nonlinear semigroup of contractionsS(t): {ie221-2}) → {ie221-3}), strongly continuous at the origin, withS(t) compact for allt>0. Then, for eachu
0 ∈ {ie221-4}) ∩U there existsT ∈ ]0,a] such that the following initial value problem: (du(t))/(dt) ∈Au(t) +F(u)(t),u(0)=u
0, has at least one integral solution on [0,T]. Some extensions and applications are also included. 相似文献
7.
Houman Owhadi 《Probability Theory and Related Fields》2003,125(2):225-258
This paper is concerned with the approximation of the effective conductivity σ(A, μ) associated to an elliptic operator ∇
xA
(x,η)∇
x
where for xℝ
d
, d≥1, A(x,η) is a bounded elliptic random symmetric d×d matrix and η takes value in an ergodic probability space (X, μ). Writing A
N
(x, η) the periodization of A(x, η) on the torus T
d
N
of dimension d and side N we prove that for μ-almost all η
We extend this result to non-symmetric operators ∇
x
(a+E(x, η))∇
x
corresponding to diffusions in ergodic divergence free flows (a is d×d elliptic symmetric matrix and E(x, η) an ergodic skew-symmetric matrix); and to discrete operators corresponding to random walks on ℤ
d
with ergodic jump rates.
The core of our result is to show that the ergodic Weyl decomposition associated to 2(X, μ) can almost surely be approximated by periodic Weyl decompositions with increasing periods, implying that semi-continuous
variational formulae associated to 2(X, μ) can almost surely be approximated by variational formulae minimizing on periodic potential and solenoidal functions.
Received: 10 January 2002 / Revised version: 12 August 2002 / Published online: 14 November 2002
Mathematics Subject Classification (2000): Primary 74Q20, 37A15; Secondary 37A25
Key words or phrases: Effective conductivity – periodization of ergodic media – Weyl decomposition 相似文献
8.
Joso Vukman 《Acta Mathematica Hungarica》2006,112(3):181-186
Summary Let X be a complex Hilbert space, let L(X) be the algebra of all bounded linear operators on X, and let A(X) ⊂ L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D: A(X) → L(X) satisfying the relation D(AA*A) = D(A) A*A + AD(A*)A + AA*D(A), for all A ∈ A(X). In this case D is of the form D(A) = AB-BA, for all A∈ A(X) and some B ∈ L(X), which means that D is a derivation. We apply this result to semisimple H*-algebras. 相似文献
9.
A Borel derivative on the hyperspace 2
X
of a compactumX is a Borel monotone mapD: 2
X
→2
X
. The derivative determines a Cantor-Bendixson type rank δ:2X → ω1 ∪ {∞} . We show that ifA⊂2
X
is analytic andZ⊂A intersects stationary many layers δ−1({ξ}), then for almost all σ,F∩δ−1({ξ}) cannot be separated fromZ ∩∪
a<ξ
δ−1({a}) (and also fromZ ∩∪
a>ξ
δ−1({a}) by anyF
σ-set. Another main result involves a natural partial order on 2
X
related to the derivative. The results are obtained in a general framework of “resolvable ranks” introduced in the paper.
During our work on this paper the second author was a Visiting Professor at the Miami University, Ohio. This author would
like to express his gratitude to the Department of Mathematics and Statistics for the hospitality. 相似文献
10.
Dieter Bothe 《Israel Journal of Mathematics》1998,108(1):109-138
Given anm-accretive operatorA in a Banach spaceX and an upper semicontinuous multivalued mapF: [0,a]×X→2
X
, we consider the initial value problemu′∈−Au+F(t,u) on [0,a],u(0)=x
0. We concentrate on the case when the semigroup generated by—A is only equicontinuous and obtain existence of integral solutions if, in particular,X* is uniformly convex andF satisfies β(F(t,B))≤k(t)β(B) for all boundedB⊂X wherek∈L
1([0,a]) and β denotes the Hausdorff-measure of noncompactness. Moreover, we show that the set of all solutions is a compactR
δ-set in this situation. In general, the extra condition onX* is essential as we show by an example in whichX is not uniformly smooth and the set of all solutions is not compact, but it can be omited ifA is single-valued and continuous or—A generates aC
o-semigroup of bounded linear operators. In the simpler case when—A generates a compact semigroup, we give a short proof of existence of solutions, again ifX* is uniformly (or strictly) convex. In this situation we also provide a counter-example in ℝ4 in which no integral solution exists.
The author gratefully acknowledges financial support by DAAD within the scope of the French-German project PROCOPE. 相似文献
11.
Hua Xin Lin 《数学学报(英文版)》2002,18(1):181-198
Let X be a connected finite CW complex and d
X
: K
0(C(X)) →ℤ be the dimension function. We show that, if A is a unital separable simple nuclear C*-algebra of TR(A) = 0 with the unique tracial state and satisfying the UCT such that K
0(A) = ℚ⊕ kerd
x
and K
1(A) = K
1(C(X)), then A is isomorphic to an inductive limit of M
n
!(C(X)).
Received April 19, 2001, Accepted April 27, 2001. 相似文献
12.
S. S. Podkorytov 《Journal of Mathematical Sciences》2009,161(3):454-459
Homotopy classes of mappings of a compact polyhedron X to the circle T form an Abelian group B(X), which is called the Bruschlinsky group and is cananically isomorphic to H
1 (X; ℤ), Let L be an Abelian group, and let f: B(X) → L be a function. One says that the order of f does not exceed r if for each mapping a: X → T the value f([a]) is ℤ-linearly expressed via the characteristic function I
r
(a): (X × T)
r
→ ℤ of (Γ
a
)
r
, where Γ
a
⊂ X × T is the graph of a. The (algebraic) degree of f is not greater than r if the finite differences of f of order r + 1 vanish. Conjecturally, the order of f is equal to the algebraic degree of f. The conjecture is proved in the case where dim X ≤ 2. Bibliography: 1 title. 相似文献
13.
Byungdo Kim 《数学学报(英文版)》2000,16(1):21-28
Abstract
Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A→A such that [D(x), x]D(x)[D(x),x] ∈ rad(A) for all x∈A. In this case, D(A) ⊆ rad (A).
The author has been supported by Kangnung National University, Research Fund, 1998 相似文献
14.
M. Akkar et R. El Harti 《Rendiconti del Circolo Matematico di Palermo》2000,49(1):103-114
LetA be a commutative Banach algebra with unit. Denote byX
A, the global spectrum ofA. There is a holomorphic functional calculusθ
A:O(X
A)→A such thatθ
A(a)=a. In this paper, we show the uniqueness of the global holomorphic functional calculus and we establish its compatibility with
Banach algebra morphisms. We also extend this holomorphic functional calculus to the case ofImc algebras.
相似文献
15.
Nedžad Limić 《Applied Mathematics and Optimization》2011,64(1):101-133
Consider a non-symmetric generalized diffusion X(⋅) in ℝ
d
determined by the differential operator $A(\mbox{\boldmath{$A(\mbox{\boldmath{. In this paper the diffusion process is approximated by Markov jump processes X
n
(⋅), in homogeneous and isotropic grids G
n
⊂ℝ
d
, which converge in distribution in the Skorokhod space D([0,∞),ℝ
d
) to the diffusion X(⋅). The generators of X
n
(⋅) are constructed explicitly. Due to the homogeneity and isotropy of grids, the proposed method for d≥3 can be applied to processes for which the diffusion tensor $\{a_{ij}(\mbox{\boldmath{$\{a_{ij}(\mbox{\boldmath{ fulfills an additional condition. The proposed construction offers a simple method for simulation of sample paths of non-symmetric
generalized diffusion. Simulations are carried out in terms of jump processes X
n
(⋅). For piece-wise constant functions a
ij
on ℝ
d
and piece-wise continuous functions a
ij
on ℝ2 the construction and principal algorithm are described enabling an easy implementation into a computer code. 相似文献
16.
S. S. Podkorytov 《Journal of Mathematical Sciences》2011,175(5):609-619
Homotopy classes of mappings of a space X to the circle T form an Abelian group B(X) (the Bruschlinsky group). If a: X → T is a continuous mapping, then [a] denotes the homotopy class of a, and I
r
(a): (X × T)
r
→
\mathbbZ \mathbb{Z} is the indicator function of the rth Cartesian power of the graph of a. Let C be an Abelian group and let f: B(X) → C be a mapping. By definition, f has order not greater than r if the correspondence I
r
(a) → f([a]) extends to a (partly defined) homomorphism from the Abelian group of Z-valued functions on (X × T)
r
to C. It is proved that the order of f equals the algebraic degree of f. (A mapping between Abelian groups has degree at most r if all of its finite differences of order r +1 vanish.) Bibliography: 2 titles. 相似文献
17.
Mikhail A. Chebotar Wen-Fong Ke Pjek-Hwee Lee Ruibin Zhang 《Monatshefte für Mathematik》2006,162(1):91-101
Let R be a ring, A = M
n
(R) and θ: A → A a surjective additive map preserving zero Jordan products, i.e. if x,y ∈ A are such that xy + yx = 0, then θ(x)θ(y) + θ(y)θ(x) = 0. In this paper, we show that if R contains
\frac12\frac{1}{2}
and n ≥ 4, then θ = λϕ, where λ = θ(1) is a central element of A and ϕ: A → A is a Jordan homomorphism. 相似文献
18.
19.
Mikhail A. Chebotar Wen-Fong Ke Pjek-Hwee Lee Ruibin Zhang 《Monatshefte für Mathematik》2006,149(2):91-101
Let R be a ring, A = M
n
(R) and θ: A → A a surjective additive map preserving zero Jordan products, i.e. if x,y ∈ A are such that xy + yx = 0, then θ(x)θ(y) + θ(y)θ(x) = 0. In this paper, we show that if R contains
and n ≥ 4, then θ = λϕ, where λ = θ(1) is a central element of A and ϕ: A → A is a Jordan homomorphism.
The third author is Corresponding author. 相似文献
20.
Let A be an Archimedean f -algebra and let N(A) be the set of all nilpotent elements of A. Colville et al. [6] proved that a positive linear map D : A → A is a derivation if and only if D(A) ì N(A){D(A)\subset N(A)} and D(A
2) = {0}, where A
2 is the set of all products ab in A. In this paper, we establish a result corresponding to the Colville–Davis–Keimel theorem for an order bounded derivation
D on an Archimedean almost f -algebra, which generalizes the results of Boulabiar [3]. 相似文献