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1.
Gert K. Pedersen 《Inventiones Mathematicae》1978,45(3):299-305
For each*-derivation of a separableC
*-algebraA and each >0 there is an essential idealI ofA and a self-adjoint multiplierx ofI such that (–ad(ix))|I< and x. 相似文献
2.
Let be an Artin algebra, let mod be the category of finitely generated -modules, and let Amod be a contravariantly finite and extension closed subcategory. For an indecomposable and not Ext-projective module CA, we compute the almost split sequence 0ABC0 in A from the almost split sequence 0DTrCEC0 in mod. Since the computation is particularly simple if the minimal right A-approximation of DTrC is indecomposable for all indecomposable and not Ext-projective CA, we manufacture subcategories A with the desired property using orthogonal subcategories. The method of orthogonal subcategories is applied to compute almost split sequences for relatively projective and prinjective modules. 相似文献
3.
LetA be a von Neumann algebra and a faithful normal state. ThenO
= {
ºAd(g
1) :g G
A
}andU
= {
ºAd(u
*) :u U
A
are homogeneous reductive spaces. IfA is aC
* algebra,e
the Jones projection of the faithful state viewed as a conditional expectation, then we prove that the similarity orbit ofe
by invertible elements ofA can be imbedded inAA in such a way thate
is carried to 1 1 and the orbit ofe
to a homogeneous reductive space and an analytic submanifold ofAA. 相似文献
4.
Takeaki Yamazaki 《Integral Equations and Operator Theory》2002,43(2):237-247
In 1951, Heinz showed the following useful norm inequality:If A, B0and XB(H), then AXB
r
X1–r
A
r
XB
r
holds for r [0, 1]. In this paper, we shall show the following two applications of this inequality:Firstly, by using Furuta inequality, we shall show an extension of Cordes inequality. And we shall show a characterization of chaotic order (i.e., logAlogB) by a norm inequality.Secondly, we shall study the condition under which
, where
is Aluthge transformation ofT. Moreover we shall show a characterization of normaloid operators (i.e.,r(T)=T) via Aluthge transformation. 相似文献
5.
The paper is a study of the limiting behaviour of the [n t]-th iterates of the well-known Post-Widder operatorsL
n, x used in the real inversion of the Laplace transform. It is shown that the limiting operators constitute a semigroup T
t;t0 of class (C
0) on a family C
,; , >0 of Banach spaces. Applications of the semigroup structure lead to a pointwise saturation theorem forL
n, x and a characterization of convex functions inC
, through an inequality involving the action ofL
n, x. 相似文献
6.
Thomas I. Seidman 《Applied Mathematics and Optimization》1984,11(1):145-152
(1) The known nullcontrollability result for boundary control ofu
t = uxx + q(x)u is generalized to consider a time-dependent coefficientq. (2) For boundary control ofu
t =Au (where it is known thatC
T
: (initial data) (optimal nullcontrol for timeT) exists for allT>0) it is shown that logC
T
=145-1 asT 0. 相似文献
7.
Summary We study some features concerning the occupation timeA
t of a d-dimensional coneC by Brownian motion. In particular, in the case whereC is convex, we investigate the asymptotic behaviour ofP(A1u0, when the Brownian motion starts at the vertex ofC. We also give the precise integral test, which decides whether a.s., lim inf
t
A
t/(tf(t))=0 or for a decreasing functionf. 相似文献
8.
For a linear sublattice of C(X), the set of all real continuous functions on the completely regular space X, we denote by A() the smallest uniformly closed and inverse-closed subalgebra of C(X) that contains . In this paper we study different methods to generate A() from . For that, we introduce some families of functions which are defined in terms of suprema or sums of certain countably many functions in . And we prove that A() is the uniform closure of each of these families. We obtain, in particular, a generalization of a known result about the generation of A() when is a uniformly closed linear sublattice of bounded functions. 相似文献
9.
For 0<1 and graphsG andH, we writeGH if any -proportion of the edges ofG span at least one copy ofH inG. As customary, we writeC
k for a cycle of lengthk. We show that, for every fixed integerl1 and real >0, there exists a real constantC=C(l, ), such that almost every random graphG
n, p withp=p(n)Cn
–1+1/2l
satisfiesG
n,p1/2+
C
2l+1. In particular, for any fixedl1 and >0, this result implies the existence of very sparse graphsG withG
1/2+
C
2l+1.The first author was partially supported by NSERC. The second author was partially supported by FAPESP (Proc. 93/0603-1) and by CNPq (Proc. 300334/93-1). The third author was partially sopported by KBN grant 2 1087 91 01. 相似文献
10.
For aC
1+ hyperbolic (cookie-cutter) Cantor setC we consider the limits of sequences of closed subsets ofR obtained by arbitrarily high magnifications around different points ofC. It is shown that a well defined set of limit models exists for the infinitesimal geometry, orscenery, in the Cantor set. IfCC} is a diffeomorphic copy ofC then the set of limit models of C is the same as that ofC. Furthermore every limit model is made of Cantor sets which areC
1+ diffeomorphic withC (for some >0, (0,1)), but not all suchC
1+ copies ofC occur in the limit models. We show the relation between this approach to the asymptotic structure of a Cantor set and Sullivan's scaling function. An alternative definition of a fractal is discussed.With 1 Figure 相似文献
11.
Wolfgang Grotz 《Monatshefte für Mathematik》1979,88(3):219-228
LetK be an algebraic number field, and for every integer K let () andd(), respectively, denote the number of relatively prime residue classes and the number of divisors of the principal ideal (). Asymptotic equalities are proved for the sums () and d
2(), where runs through certain finite sets of integers ofK. 相似文献
12.
Some Landau's type inequalities for infinitesimal generators 总被引:3,自引:0,他引:3
Summary Lett T(t) be a strongly continuous contraction semigroup on a complex Banach space and letA be its infinitesimal generator. We prove that, forx D(A
3), the following inequalities hold true: Ax3 243/8 x2A
3
x, A
2
x 24 xA
3
x2. Ift T(t) is a contraction group (resp. cosine function) we get the analogous but better inequalities with constants 9/8 and 3 (resp. 81/40 and 72/25) instead of 243/8 and 24. We consider also uniformly bounded semigroups, groups and cosine functions. 相似文献
13.
Graham R. Brightwell 《Order》1985,2(2):129-144
Posets A, BX×X, with X finite, are said to be universally correlated (AB) if, for all posets R over X, (i.e., all posets RY×Y with XY), we have P(RA) P(RB)P(RAB) P(R). Here P(RA), for instance, is the probability that a randomly chosen bijection from Y to the totally ordered set with |Y| elements is a linear extension of RA. We show that AB iff, for all posets R over X, P(RA) P(RB)P(RAB) P(R(AB)).Winkler proved a theorem giving a necessary and sufficient condition for AB. We suggest an alteration to his proof, and give another condition equivalent to AB.Daykin defined the pair (A, B) to be universally negatively correlated (A B) if, for all posets R over X, P(RA) P(RB)P(RAB) P(R(AB)). He suggested a condition for AB. We give a counterexample to that conjecture, and establish the correct condition. We write AB if, for all posets R over X, P(RA) P(RB)P(RAB) P(R). We give a necessary and sufficient condition for AB.We also give constructive techniques for listing all pairs (A, B) satisfying each of the relations AB, AB, and AB. 相似文献
14.
We present two convergence theorems for Hamilton-Jacobi equations and we apply them to the convergence of approximations and perturbations of optimal control problems and of two-players zero-sum differential games. One of our results is, for instance, the following. LetT andT
h be the minimal time functions to reach the origin of two control systemsy = f(y, a) andy = f
h
(y, a), both locally controllable in the origin, and letK be any compact set of points controllable to the origin. If f
h –f Ch, then |T(x) – T
h
(x)| C
K
h
, for all x K, where is the exponent of Hölder continuity ofT(x). 相似文献
15.
Mario Petrich 《Monatshefte für Mathematik》1993,116(3-4):287-298
For a Rees matrix semigroupS with normalized sandwich matrix and C(S), the congruence lattice ofS, we consider the lattice generated by {itpTl, pK, pTr, ptl, pk, ptr}. HerepT
1 andpt
l
are the upper and lower ends of the interval which makes up the
i
-class of ,
i
being the left trace relation onC(S). The remaining symbols have the analogous meaning relative to the kernel and the right trace relations. We also consider the lattice generated by {T
l, K, Tr, tl, k, tr} where and are the equality and the universal relations onS, respectively. In both cases, we find lattices freest relative to these lattices and represent them as distributive lattices with generators and relations.With 3 Figures 相似文献
16.
Criteria are derived for ergodicity and geometric ergodicity of Markov processes satisfyingX
n+1
=f(X
n
)+(X
n
)
n+1
, wheref, are measurable, {
n
} are i.i.d. with a (common) positive density,E|
n
|>. In the special casef(x)/x has limits, , asx– andx+, respectively, it is shown that <1, <1, <1 is sufficient for geometric ergodicity, and that <-1, 1, 1 is necessary for recurrence. 相似文献
17.
Tomasz Rolski 《Probability Theory and Related Fields》1990,84(1):27-37
Summary We discuss in this paper a non-homogeneous Poisson process A driven by an almost periodic intensity function. We give the stationary version A
* and the Palm version A
0 corresponding to A
*. Let (T
i
,i) be the inter-point distance sequence in A and (T
i
0
,i) in A
0. We prove that forj, the sequence (T
i+j,i) converges in distribution to (T
i
0
,i). If the intensity function is periodic then the convergence is in variation. 相似文献
18.
G. Wanner 《BIT Numerical Mathematics》1980,20(1):102-106
Following the slogan a picture is better than thousand data, for restricted Padé approximations with one realm-fold pole atz=1/ of orderm, we plot the error constants, the maximal error for negative realz as functions of, as well as the regions ofA- resp.A(0)-stability. 相似文献
19.
ARANDOMLYWEIGHTEDESTIMATEOFTHEPOPULATION MEANCHENXIRU(陈希孺)JINMINGZHONG(金明仲)(GraduateSchool,UniversityofScienceandTechnolapyof... 相似文献
20.
IfG is a second countable locally compact group acting continuously on a separableC
*-algebraA, then every primitive ideal of the crossed productC
*
(G, A) is contained in an induced primitive ideal, and ifG is amenable, equality holds. Thus ifG is amenable and acts freely on Prim(A), the generalized Effros-Hahn conjecture holds: there is a canonical bijection between primitive ideals ofC
*
(G, A) andG-quasi-orbits in Prim(A). Applications to the Mackey machine for a non-regularly embedded normal subgroup of a locally compact group are discussed. The proof of the theorem is based on a local cross-section result together with Mackey's original methods.The authors were partially supported by National Science Foundation Research GrantsThe first-named author would like to thank the Department of Mathematics, University of Pennsylvania, for its warm hospitality during his 1977–78 stay, during which time this research was conducted 相似文献