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1.
We consider the semi-group Ext(A, B) of extensions of a separable C
*-algebra A by a stable C
*-algebra B modulo unitary equivalence and modulo asymptotically split extensions. This semi-group contains the group Ext–1/2(A, B) of invertible elements (i.e. of semi-invertible extensions). We show that the functor Ext–1/2(A, B) is homotopy invariant and that it coincides with the functor of homotopy classes of asymptotic homomorphisms from C
A to M(B) that map S
A
C(
)
A into B. 相似文献
2.
The measure
(A) of nonconvexity for a bounded subset A of a normed linear space L is the Hausdorff distance between A and the convex hull coA. It is proved that if L is an L
p-space, then
, where d(A) is the diameter of A and
. Furthermore, this estimate is sharp. Bibliography: 6 titles. 相似文献
3.
In this paper we characterize the situation wherein a subspaceS of a separable Hilbert state space is holdable under the abstract linear autonomous control system
, whereA is the infinitesimal generator of aC
0-semigroup of operators and whereB is a bounded linear operator mapping a Hilbert space intoX. WhenS
D(A*) is dense inS
, it is shown that a necessary (but insufficient) condition for holdability is (1):
. A stronger condition than (1) is shown to be sufficient for a type of approximate holdability. In the finite dimensional setting, (1) reduces to (A, B)-invariance, which is known to be equivalent to the existence of a (bounded) linear feedback control law which achieves holdability inS. We prove that this equivalence holds in infinite dimensions as well, whenA is bounded and the linear spacesS, B andS+ B are closed.In the unbounded case, our results are illustrated by the shift semigroup and by the heat equation on an infinite rod with distributed controls. In the bounded case, our example is an integro-differential control system.Research sponsored by the National Research Council of Canada under Grant A7271.Research sponsored by the National Research Council of Canada under Grant A4641. 相似文献
4.
Let
be a unital C*-algebra and G the group of units of
. A geometrical study of the action of G over the set
+ of all positive elements of
is presented. The orbits of elements with closed range by this action are provided with a structure of differentiable homogeneous space with a natural connection. The orbits are partitioned in 'components' which also have a rich geometrical structure. 相似文献
5.
Sierpiski proved that every countable set of mappings on an infinite set
X is
contained in a 2-generated subsemigroup of the semigroup of all mappings on
X. In this
paper we prove that every countable set of endomorphisms of an algebra
which has an infinite basis (independent generating set) is contained in a 2-generated subsemigroup
of the semigroup of all endomorphisms of
. 相似文献
6.
O. V. Sarafanov 《Journal of Mathematical Sciences》2004,120(2):1195-1239
The C
*-algebra
generated by the operators of pseudodifferential boundary value problems on a manifold
with smooth closed disjoint edges and boundary
is studied. The operators act in the space L
2(
)
L
2(
). The goal of this paper is to describe all (up to an equivalence) irreducible representations of the algebra
Bibliography: 12 titles. 相似文献
7.
A. M. Gomilko 《Ukrainian Mathematical Journal》2004,56(8):1212-1226
We consider the problem of estimates for the powers of the Cayley transform V = (A + I)(A - I)–1 of the generator of a uniformly bounded C
0-semigroup of operators e
tA
, t 0, that acts in a Hilbert space H. In particular, we establish the estimate
. We show that the estimate
is true in the following cases: (a) the semigroups e
tA
and
are uniformly bounded; (b) the semigroup e
tA
uniformly bounded for t is analytic (in particular, if the generator of the semigroup is a bounded operator).Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 8, pp. 1018–1029, August, 2004. 相似文献
8.
Vlad Ionescu 《Integral Equations and Operator Theory》1999,34(1):45-55
Based on the Ben Artzi-Gohberg result concerning the equivalence between the invertibility of theL
2-operator
and the exponential dichotomic evolution defined byA(t), the time-varying counterpart of the Redheffer theorem is considered under relaxed conditions. 相似文献
9.
I. Dejaiffe J. P. Tignol D. W. Lewis 《Rendiconti del Circolo Matematico di Palermo》2000,49(2):325-342
The notion of Witt equivalence of central simple algebras with involution is introduced. It is shown that the standard invariants,
i.e. the discriminant, the signature and the Clifford algebra, depend only on the Witt class of the algebra with involution.
For a given filedF the tensor product is used to construct a semigroup
and this semigroup is shown to have properties analogous to the multiplicative properties of the Witt ring of quadratic forms
overF. 相似文献
10.
11.
This paper considers feedback stabilization for the semilinear control system
HereA is the infinitesimal generator of a linearC
0 semigroup of contractions on a Hilbert spaceH andB : H H is a nonlinear operator. A sufficient condition for feedback stabilization is given and applications to hyperbolic boundary value problems are presented.This research was sponsored in part by grant no. MCS76-07012 from the U.S. National Science Foundation. 相似文献
12.
We present sufficient conditions on a Gaussian Mehler semigroup on a reflexive Banach space Eto be induced by a single positive symmetric operator Q \in
, and give a counterexample which shows that this representation theorem is false in every nonreflexive Banach space with a Schauder basis. We also show that the transition semigroup of a Gaussian Mehler semigroup on a separable Banach space Eacts in a pointwise continuous way, uniformly on compact subsets of E, in the space BUC(E) of bounded uniformly continuous real-valued funtions on E. The transition semigroup is shown to be strongly continuous on BUC(E) if and only if S(t) = Ifor all t 0 相似文献
13.
Marco Romito 《Monatshefte für Mathematik》1998,126(4):329-352
Given an open bounded convex subset of
p
, a strictly elliptic differential operatorL and a continuous function
, and denoted withT
L the Dirichlet operator associated withL, the Lototsky-Schnabl operators associated withT
L and are investigated. In particular, conditions are established which ensure the existence of a Feller semigroup represented by limit of powers of these operators. Then the analytic expression of the infinitesimal generator is determined and some properties of the semigroup are deduced. Finally, the saturation class of Lototsky-Schnabl operators is determined.Work supported by a C.N.R. Research Grant (n. 201.19.1, November 30, 1994) 相似文献
14.
Xu Cheng 《Bulletin of the Brazilian Mathematical Society》2000,31(2):225-239
We prove that a complete noncompact oriented strongly stable hypersurfaceM
n
with cmc (constant mean curvature)H in a complete oriented manifoldN
n+1
with bi-Ricci curvature, satisfying
alongM, admits no nontrivialL
2 harmonic 1-forms. This implies ifM
n
(2n4) is a complete noncompact strongly stable hypersurface in hyperbolic spaceH
n+1(–1) with cmc
, there exist no nontrivialL
2 harmonic 1-forms onM. We also classify complete oriented strongly stable surfaces with cmcH in a complete oriented manifoldN
3 with scalar curvature
satisfying
. 相似文献
15.
In this paper, we consider equations of the form
, where
is a function with values in the Hilbert space
, the operator B is symmetric, and the operator A is uniformly positive and self-adjoint in
. The linear operator
generating the C
0-semigroup in the energy space
is associated with this equation. We prove that this semigroup is exponentially stable if the operator B is uniformly positive and the operator A dominates B in the sense of quadratic forms. 相似文献
16.
Christine Bachoc Renaud Coulangeon Gabriele Nebe 《Journal of Algebraic Combinatorics》2002,16(1):5-19
We introduce the notion of a t-design on the Grassmann manifold
of the m-subspaces of the Euclidean space
n
. It generalizes the notion of antipodal spherical design which was introduced by P. Delsarte, J.-M. Goethals and J.-J. Seidel. We characterize the finite subgroups of the orthogonal group which have the property that all its orbits are t-designs. Generalizing a result due to B. Venkov, we prove that, if the minimal m-sections of a lattice L form a 4-design, then L is a local maximum for the Rankin function
n,m
. 相似文献
17.
Perturbation of Dirichlet forms by measures 总被引:8,自引:0,他引:8
Perturbations of a Dirichlet form
by measures are studied. The perturbed form
––++ is defined for – in a suitable Kato class and + absolutely continuous with respect to capacity. L
p-properties of the corresponding semigroups are derived by approximating – by functions. For treating +, a criterion for domination of positive semigroups is proved. If the unperturbed semigroup has L
p
-L
q
-smoothing properties the same is shown to hold for the perturbed semigroup. If the unperturbed semigroup is holomorphic on L
1 the same is shown to be true for the perturbed semigroup, for a large class of measures. 相似文献
18.
Thierry Coulhon 《Potential Analysis》1992,1(4):343-353
One shows the equivalence between an abstract form of a Gagliardo-Nirenberg inequality and an estimate of the decay of the L
1–L
norm of a semigroup of operators. This equivalence, contrary to the one with the classical Sobolev inequalities, allows the treatment of situations where the decay is exponential. Related results and applications are given.
Cet article a pu être terminé pendant un séjour de l'auteur à l'université d'Edimbourg. 相似文献
19.
A (k,n)-arc in PG(2,q) is usually defined to be a set
of k points in the plane such that some line meets
in n points but such that no line meets
in more than n points. There is an extensive literature on the topic of (k,n)-arcs. Here we keep the same definition but allow
to be a multiset, that is, permit
to contain multiple points. The case k=q
2+q+2 is of interest because it is the first value of k for which a (k,n)-arc must be a multiset. The problem of classifying (q
2+q+2,q+2)-arcs is of importance in coding theory, since it is equivalent to classifying 3-dimensional q-ary error-correcting codes of length q
2+q+2 and minimum distance q
2. Indeed, it was the coding theory problem which provided the initial motivation for our study. It turns out that such arcs are surprisingly rich in geometric structure. Here we construct several families of (q
2+q+2,q+2)-arcs as well as obtain some bounds and non-existence results. A complete classification of such arcs seems to be a difficult problem. 相似文献
20.
Summary We show that the set
of equivalence classes of synchronously automatic structures on a geometrically finite hyperbolic groupG is dense in the product of the sets
over all maximal parabolic subgroupsP. The set
of equivalence classes of biautomatic structures onG is isomorphic to the product of the sets
over the cusps (conjugacy classes of maximal parabolic subgroups) ofG. Each maximal parabolicP is a virtually abelian group, so
and
were computed in [NS1].We show that any geometrically finite hyperbolic group has a generating set for which the full language of geodesics forG is regular. Moreover, the growth function ofG with respect to this generating set is rational. We also determine which automatic structures on such a group are equivalent to geodesic ones. Not all are, though all biautomatic structures are.Oblatum 14-VI-1993 & 4-I-1994Both authors acknowledge support from the NSF for this research. 相似文献