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We characterize generators of sub-Markovian semigroups onL p () by a version of Kato's inequality. This will be used to show (under precise assumptions) that the semigroup generated by a matrix operatorA=(A ij )1i,jn on (L p ()) n is sub-Markovian if and only if the semigroup generated by the sum of each rowA i 1+...+A in (1in), is sub-Markovian. The corresponding result on (C 0(X)) n characterizes dissipative operator matrices.
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3.
We study error bounds in the operator norm topology for the Trotter-Kato product formula. We prove that they depend on fractional power conditions (domains and relative boundedness) for operators involved in this formula.Dedicated to Professor M.Sh.BIRMAN on the occassion of his 70th birthday.  相似文献   

4.
The product of operators with closed range in Hilbert C-modules   总被引:1,自引:0,他引:1  
Suppose T and S are bounded adjointable operators with close range between Hilbert C-modules, then TS has closed range if and only if Ker(T)+Ran(S) is an orthogonal summand, if and only if Ker(S)+Ran(T) is an orthogonal summand. Moreover, if the Dixmier (or minimal) angle between Ran(S) and Ker(T)∩[Ker(T)∩Ran(S)] is positive and is an orthogonal summand then TS has closed range.  相似文献   

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For a nonempty closed set C in a real normed vector space X and an inequality solution set, we present several sufficient conditions for the tangent and contingent cones to their intersection to contain the intersections of the corresponding cones. We not only express the contingent cone to a solution set of inequalities and equalities by the directional (or Fréchet) derivatives of the active inequality constraint functions and the Fréchet derivatives of the equality constraint functions but also the tangent cone by the Clarke (or lower Dini, or upper Dini) derivatives of the active inequality constraint functions and the directional derivatives of the equality constraint functions. By using a simple property of the function dCdCc, we characterize these cones by the hypertangent and hypercontingent vectors to the set C. Furthermore, these results allow us to present new constraint qualifications for the Karush-Kuhn-Tucker conditions.  相似文献   

7.
The set system satisfiesProperty B if there exists a partitionX 1X 2=X such that any element of intersects both classes. Here, we study the following problem: We are givenk set systems on the underlying setX, and we are seeking ak-partition ofX such that any element of theith set system intersectsX i for everyi.The paper received its final form when the author enjoyed the hospitality of L.A. Székely of the University of South Carolina, Columbia, South Carolina, USA. The research was partially supported by the Hungarian Scientific Fund, Grant no. T16358.  相似文献   

8.
The symmetric chain decomposition of the lattice of divisors,D N, is applied to prove results about the strict unimodality of the Whitney numbers ofD N, about minimum interval covers for the union of consecutive rank-sets ofD N, and about the distribution of sums of vectors in which each vector can be included several times (an extension of the famous Littlewood-Offord problem)Research supported in part by NSA/MSP GrantMDA904-92H3053.  相似文献   

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Roger Labahn 《Order》1992,9(4):349-355
In the n-dimensional cube, we determine the maximum size of antichains having a lower shadow of exactly m elements in the k-th level.  相似文献   

11.
The adjoint of aC 0-semigroup on a Banach spaceX induces a locally convex σ(X,X )-topology inX, which is weaker than the weak topology ofX. In this paper we study the relation between these two topologies. Among other things a class of subsets ofX is given on which they coincide. As an application, an Eberlein-Shmulyan type theorem is proved for the σ(X,X )-topology and it is shown that the uniform limit of σ(X,X )-compact operators is σ(X,X )-compact. Finally our results are applied to the problem when the Favard class of a semigroup equals the domain of the infinitesimal generator.  相似文献   

12.
In the present paper we study the error estimate in the operator norm for the Trotter-Kato product formula, having an intention to apply the obtained result to Schrödinger semigroups with singular potentials.  相似文献   

13.
Spline quasi-interpolants are practical and effective approximation operators. In this paper, we construct QIs with optimal approximation orders and small infinity norms called near-best discrete quasi-interpolants which are based on Ω-splines, i.e. B-splines with octagonal supports on the uniform four-directional mesh of the plane. These quasi-interpolants are exact on some space of polynomials and they minimize an upper bound of their infinity norms depending on a finite number of free parameters. We show that this problem has always a solution, in general nonunique. Concrete examples of such quasi-interpolants are given in the last section.  相似文献   

14.
The main concern of this paper is the perturbation problem for oblique projection generalized inverses of closed linear operators in Banach spaces. We provide a new stability characterization of oblique projection generalized inverses of closed linear operators under T-bounded perturbations, which improves some well known results in the case of the closed linear operators under the bounded perturbation or that the perturbation does not change the null space.  相似文献   

15.
The present contribution deals with the Stokes operator Aq on Lqσ(Ω), 1<q<∞, where Ω is an exterior domain in ℝ2 of class C2. It is proved that Aq admits a bounded H-calculus. This implies the existence of bounded imaginary powers of Aq, which has several important applications. – So far this property was only known for exterior domains in ℝn, n≥3. – In particular, this shows that Aq has maximal regularity on Lqσ(Ω). For the proof the resolvent (λ+Aq)−1 has to be analyzed for |λ|→∞ and λ→0. For large λ this is done using an approximate resolvent based on the results of [3], which were obtained by applying the calculus of pseudodifferential boundary value problems. For small λ we analyze the representation of the resolvent developed in [11] by a potential theoretical method.  相似文献   

16.
In anydense posetP (and in any Boolean lattice in particular) every maximal antichainS may be partitioned into disjoint subsetsS 1 andS 2, such that the union of the downset ofS 1 with the upset ofS 2 yields the entire poset:D(S 1) U (S 2) =P. To find a similar splitting of maximal antichains in posets is NP-hard in general.Research was partially carried out when the second author visited the first author in Bielefeld and it was partially supported by OTKA grant T016358  相似文献   

17.
Let T = U|T| and S = V|S| be the polar decompositions. In this paper, we shall obtain the polar decomposition of TS as TS = UWV|TS|, where |T||S*| = W||T||S*|| is the polar decomposition. Next, we shall show that TS = UV|TS| is the polar decomposition if and only if |T| commutes with |S*|. Lastly, we shall apply this result to binormal and centered operators. We shall obtain characterizations of these operator classes from the viewpoint of the polar decomposition.  相似文献   

18.
This paper deals with perturbations of the Ornstein-Uhlenbeck operator on L2-spaces with respect to a Gaussian measure μ. We perturb the generator of the Ornstein-Uhlenbeck semigroup by a certain unbounded, non-linear drift, and show various properties of the perturbed semigroup such as compactness and positivity. Strong Feller property, existence and uniqueness of an invariant measure are discussed as well.  相似文献   

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This paper deals with the local nonsolvability in Schwartz distribution spaceD′ ofm-order partial differential operator whose principal symbol is them-th power of locally solvable and hypoelliptic Mizohata type operator.
Sunto Questo lavoro tratta la nonrisolubilità locale nello spazio delle distribuzioni di SchwartzD′ degli operatori alle derivate parziali di ordinem il cui simbolo principale è lam-sima potenza dell'operatore tipo Mizohata localmente risolubile ed ipoellittico.
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