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1.
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
2.
A. N. Dyogtev 《Algebra and Logic》1996,35(2):80-85
Let A⊆N={0,1,2,...} and β be an n-ary Boolean function. We call A a β-implicatively selector (β-IS) set if there exists an
n-ary selector general recursive function f such that (∀x1,...,xn)(β(χ(x1),...,χ(xn))=1⟹f(x1,...,xn)∈A), where χ is the characteristic function of A. Let F(m), m≥1, be the family of all d
m+1
*
-IS sets, where
, F(0)=N, and F(∞) is the class of all subsets in N. The basic result of the article says that the family of all β-IS sets coincides with one
of F(m), m≥0, or F(∞), and, moreover, the inclusions F(0)⊂F(1)⊂...⊂F(∞) hold.
Translated fromAlgebra i Logika, Vol. 35, No. 2, pp. 145–153, March–April, 1996. 相似文献
3.
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
4.
We study the Banach spacesX with the following property: there is a numberδ in ]0,1[ such that for some constantC, any finite dimensional subspaceE ⊂X contains a subspaceF ⊂E with dimF≧δ dimE which isC-isomorphic to a Euclidean space. We show that if this holds for someδ in ]0,1[ then it also holds for allδ in ]0,1[ and we estimate the functionC=C(δ). We show that this property holds iff the “volume ratio” of the finite dimensional subspaces ofX are uniformly bounded. We also show that (althoughX can have this property without being of cotype 2)L
2(X) possesses this property iffX if of cotype 2. In the last part of the paper, we study theK-convex spaces which have a dual with the above property and we relate it to a certain extension property. 相似文献
5.
M. M. Sheremeta 《Ukrainian Mathematical Journal》1996,48(3):460-466
We prove that, for every sequence (a
k) of complex numbers satisfying the conditions Σ(1/|a
k
|) < ∞ and |a
k+1| − |a
k
| ↗ ∞ (k → ∞), there exists a continuous functionl decreasing to 0 on [0, + ∞] and such thatf(z) = Π(1 −z/|a
k
|) is an entire function of finitel-index. 相似文献
6.
Subhash J. Bhatt 《Proceedings Mathematical Sciences》2006,116(2):161-173
Given anm-tempered strongly continuous action α of ℝ by continuous*-automorphisms of a Frechet*-algebraA, it is shown that the enveloping ↡-C
*-algebraE(S(ℝ, A∞, α)) of the smooth Schwartz crossed productS(ℝ,A
∞, α) of the Frechet algebra A∞ of C∞-elements ofA is isomorphic to the Σ-C
*-crossed productC
*(ℝ,E(A), α) of the enveloping Σ-C
*-algebraE(A) ofA by the induced action. WhenA is a hermitianQ-algebra, one getsK-theory isomorphismRK
*(S(ℝ, A∞, α)) =K
*(C
*(ℝ,E(A), α) for the representableK-theory of Frechet algebras. An application to the differential structure of aC
*-algebra defined by densely defined differential seminorms is given. 相似文献
7.
Let p ∈ {1, ∞}. We show that any continuous linear operator T from A1 (a) to Ap (b) is tame, i.e., there exists a positive integer c such that sup x||Tx||k/|x|ck ∞ for every k ∈ N. Next we prove that a similar result holds for operators from A∞(a) to Ap(b) if and only if the set Mb,a of all finite limit points of the double sequence (bi /aj ) i,j∈N is bounded. Finally we show that the range of every tame operator from A∞(a) to A∞(b) has a Schauder basis. 相似文献
8.
S. V. Kislyakov 《Journal of Mathematical Sciences》1981,16(3):1102-1108
Let A be a closed subalgebra of the complex Banach algebra C(S), containing the constant functions. We assume that one has
found a probability measureμ on S and a function F from L∞(μ) such that: 1)|F|= 1 a.e. relative to μ; 2) F
μ
ε A1; 3) F is a limit point of the unit ball of the algebra A in the topology δ(L∞(μ), L1(μ)). One proves in the paper that under these conditions the space A** contains a complement space, isometric to H∞. The measure μ and the function F, satisfying the conditions l)-3) indeed exist if the maximal ideal space of the algebra
A contains a non-one-point part (and it is very likely that such aμ. and F exist whenever the algebra A is not self-adjoint). Thus, the above-formulated result allows us to extend A. Pelczynski's
theorem (Ref, Zh. Mat., 1975, 1B894) regarding the space H∞ to a very broad class of uniform algebras.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 65, pp. 80–89, 1976. 相似文献
9.
V. M. Petrogradsky 《Monatshefte für Mathematik》2006,49(6):243-249
Let R be a finitely generated associative algebra with unity over a finite field
\Bbb Fq{\Bbb F}_q
. Denote by a
n
(R) the number of left ideals J ⊂ R such that dim R/J = n for all n ≥ 1. We explicitly compute and find asymptotics of the left ideal growth for the free associative algebra A
d
of rank d with unity over
\Bbb Fq{\Bbb F}_q
, where d ≥ 1. This function yields a bound a
n
(R) ≤ a
n
(A
d
),
n ? \Bbb Nn\in{\Bbb N}
, where R is an arbitrary algebra generated by d elements. Denote by m
n
(R) the number of maximal left ideals J ⊂ R such that dim R/J = n, for n ≥ 1. Let d ≥ 2, we prove that m
n
(A
d
) ≈ a
n
(A
d
) as n → ∞. 相似文献
10.
M. M. Sheremeta 《Ukrainian Mathematical Journal》1999,51(8):1296-1302
We establish the relation between the increase of the quantityM(σ,F) = ∣a
0∣ + ∑
n=1
∞
∣a
n
∣ exp (σλ
n
) and the behavior of sequences (|a
n
|) and (λ
n
), where (λ
n
) is a sequence of nonnegative numbers increasing to + ∞, andF(s) =a
0 + ∑
n=1
∞
a
n
e
sλn
,s=σ+it, is the Dirichlet entire series.
Lviv University, Lviv. Translated from Ukrainskii Matematicheskii Zhurmal, Vol. 51, No. 8, pp. 1149–1153, August, 1999. 相似文献
11.
Let F be a field, let A be a vector space over F, and let GL(F, A) be the group of all automorphisms of the space A. If H is a subgroup of GL(F, A), then we set aug dimF (H) = dimF (A(ωFH)), where ωFH is the augmentation ideal of the group ring FH. The number aug dimF (H) is called the augmentation dimension of the subgroup H. In the present paper, we study locally solvable linear groups with minimality condition for subgroups of infinite augmentation
dimension.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1476–1489, November, 2005. 相似文献
12.
Ji-pu Ma Tseng Yaun Rong Functional Analysis Research Center Harbin Normal University Harbin China 《中国科学A辑(英文版)》2007,50(9):1233-1239
Let E, F be two Banach spaces, and B(E, F), Φ(E, F), SΦ(E, F) and R(E,F) be the bounded linear, Fredholm, semi-Frdholm and finite rank operators from E into F, respectively. In this paper, using the continuity characteristics of generalized inverses of operators under small perturbations, we prove the following result Let ∑ be any one of the following sets {T ∈ Φ(E, F) IndexT =const, and dim N(T) = const.}, {T ∈ SΦ(E, F) either dim N(T) = const. < ∞ or codim R(T) = const.< ∞} and {T ∈ R(E, F) RankT =const.<∞}. Then ∑ is a smooth submanifold of B(E, F) with the tangent space TA∑ = {B ∈ B(E,F) BN(A) (∪) R(A)} for any A ∈ ∑. The result is available for the further application to Thom's famous results on the transversility and the study of the infinite dimensional geometry. 相似文献
13.
A. D. Baranov 《Journal of Mathematical Sciences》2000,101(2):2881-2913
The boundedness conditions for the differentiation operator in Hilbert spaces of entire functions (Branges spaces) and conditions
under which the embedding Kи⊂L2(μ) holds in spaces Kи associated with the Branges spacesH(E) are studied. Measure μ such that the above embedding is isometric are of special interest. It turns out that the condition
E'/E∈H∞(C+) is sufficient for the boundedness of the differentiation operator inH(E). Under certain restrictions on E, this condition is also necessary. However, this fact fails in the general case, which is
demonstrated by the counterexamples constructed in this paper. The convex structure of the set of measures μ such that the
embedding KE
*
/E⊂L2(μ) is isometric (the set of such measures was described by de Brages) is considered. Some classes of measures that are extreme
points in the set of Branges measures are distinguished. Examples of measures that are not extreme points are also given.
Bibliography: 7 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 19, 1999, pp. 27–68. 相似文献
14.
Aissa Guesmia 《Israel Journal of Mathematics》2001,125(1):83-92
We consider in this paper the evolution systemy″−Ay=0, whereA =∂
i(aij∂j) anda
ij ∈C
1 (ℝ+;W
1,∞ (Ω)) ∩W
1,∞ (Ω × ℝ+), with initial data given by (y
0,y
1) ∈L
2(Ω) ×H
−1 (Ω) and the nonhomogeneous conditiony=v on Γ ×]0,T[. Exact controllability means that there exist a timeT>0 and a controlv such thaty(T, v)=y′(T, v)=0. The main result of this paper is to prove that the above system is exactly controllable whenT is “sufficiently large”. Moreover, we obtain sharper estimates onT. 相似文献
15.
Let 𝔄 denote the C*-algebra of bounded operators on L
2 ℝ generated by: (i) all multiplications a(M) by functions a∈C[ − ∞, + ∞], (ii) all multiplications by 2π-periodic continuous functions, and (iii) all operator of the form F
−1
b(M)F, where F denotes the Fourier transform and b∈C[ − ∞, + ∞]. A given A ∈ 𝔄 is a Fredholm operator if and only if σ(A) and γ(A) are invertible, where σ denotes the continuous extension of the usual principal symbol, while γ denotes an operator-valued “boundary principal symbol” (the “boundary” here consists of two copies of the circle, one at
each end of the real line). We give two proofs of the fact that K
0(𝔄) is isomorphic to ℤ and that K
1(𝔄) is isomorphic to ℤ ⊕ ℤ . We do it first by computing the connecting mappings in the six-term exact sequence associated
to σ. For the second proof, we show that the image of γ is isomorphic to the direct sum of two copies of the crossed product
, where α denotes the translation-by-one automorphism. Its K-theory can be computed using the Pimsner–Voiculescu exact sequence,
and that information suffices for the analysis of the standard cyclic exact sequence associated to γ.
Received: February 2006 相似文献
16.
Jean-Pierre Levinski 《Israel Journal of Mathematics》1984,48(2-3):225-243
We consider various forms of the Conjecture of Chang. Part A constitutes an introduction. Donder and Koepke have shown that
if ρ is a cardinal such that ρ ≧ ω1, and (ρ++,ρ+↠(ρ+, ρ), then 0+ exists. We obtain the same conclusion in Part B starting from some other forms of the transfer hypothesis. As typical corollaries,
we get:
Theorem A.Assume that there exists cardinals λ, κ, such that λ ≧
K
+ ≧ω2 and (λ+, λ)↠(K
+,K. Then 0+ exists.
Theorem B.Assume that there exists a singularcardinal κ such that(K
+,K↠(ω1, ω0. Then 0+ exists.
Theorem C.Assume that (λ
++, λ). Then 0+ exists (also ifK=ω
0.
Remark. Here, as in the paper of Donder and Koepke, “O+ exists” is a matter of saying that the hypothesis is strictly stronger than “L(μ) exists”. Of course, the same proof could give a few more sharps overL(μ), but the interest is in expecting more cardinals, coming from a larger core model.
Theorem D.Assume that (λ
++, λ)↠(K
+, K) and thatK≧ω
1. Then 0+ exists.
Remark 2. Theorem B is, as is well-known, false if the hypothesis “κ is singular” is removed, even if we assume thatK≧ω
2, or that κ is inaccessible. We shall recall this in due place.
Comments. Theorem B and Remark 2 suggest we seek the consistency of the hypothesis of the form:K
+, K↠(ωn +1, ωn), for κ singular andn≧0. 0266 0152 V 3
The consistency of several statements of this sort—a prototype of which is (N
ω+1,N
ω)↠(ω1, ω0) —have been established, starting with an hypothesis slightly stronger than: “there exists a huge cardinal”, but much weaker
than: “there exists a 2-huge cardinal”. These results will be published in a joint paper by M. Magidor, S. Shelah, and the
author of the present paper. 相似文献
17.
For a set A, let P(A) be the set of all finite subset sums of A. We prove that if a sequence B={b
1<b
2<⋯} of integers satisfies b
1≧11 and b
n+1≧3b
n
+5 (n=1,2,…), then there exists a sequence of positive integers A={a
1<a
2<⋯} for which P(A)=ℕ∖B. On the other hand, if a sequence B={b
1<b
2<⋯} of positive integers satisfies either b
1=10 or b
2=3b
1+4, then there is no sequence A of positive integers for which P(A)=ℕ∖B. 相似文献
18.
Given a C*-normed algebra A which is either a Banach *-algebra or a Frechet *-algebra, we study the algebras Ω∞
A and Ωε
A obtained by taking respectively the projective limit and the inductive limit of Banach *-algebras obtained by completing
the universal graded differential algebra Ω*A of abstract non-commutative differential forms over A. Various quantized integrals on Ω∞
A induced by a K-cycle on A are considered. The GNS-representation of Ω∞
A defined by a d-dimensional non-commutative volume integral on a d
+-summable K-cycle on A is realized as the representation induced by the left action of A on Ω*A. This supplements the representation A on the space of forms discussed by Connes (Ch. VI.1, Prop. 5, p. 550 of [C]). 相似文献
19.
YU JIARONG 《高校应用数学学报(英文版)》1995,10(4):361-366
WEIGHTEDAPPROXIMATIONOFRANDOMFUNCTIONSYUJIARONGAbstract:Let(Ω,A,P)beaprobabilityspace,X(t,ω)arandomfunctioncontinuousinprobab... 相似文献
20.
Rumi Shindo 《Central European Journal of Mathematics》2010,8(1):135-147
Let A and B be uniform algebras. Suppose that α ≠ 0 and A
1 ⊂ A. Let ρ, τ: A
1 → A and S, T: A
1 → B be mappings. Suppose that ρ(A
1), τ(A
1) and S(A
1), T(A
1) are closed under multiplications and contain expA and expB, respectively. If ‖S(f)T(g) − α‖∞ = ‖ρ(f)τ(g) − α‖∞ for all f, g ∈ A
1, S(e
1)−1 ∈ S(A
1) and S(e
1) ∈ T(A
1) for some e
1 ∈ A
1 with ρ(e
1) = 1, then there exists a real-algebra isomorphism $
\tilde S
$
\tilde S
: A → B such that $
\tilde S
$
\tilde S
(ρ(f)) = S(e
1)−1
S(f) for every f ∈ A
1. We also give some applications of this result. 相似文献