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When A∈B(H) and B∈B(K) are given, we denote by MC the operator matrix acting on the infinite-dimensional separable Hilbert space H⊕K of the form In this paper, for given A and B, the sets and ?C∈Inv(K,H)σl(MC) are determined, where σl(T),Bl(K,H) and Inv(K,H) denote, respectively, the left spectrum of an operator T, the set of all the left invertible operators and the set of all the invertible operators from K into H. 相似文献
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Marian Nowak 《Journal of Mathematical Analysis and Applications》2009,349(2):361-366
Let L(X,Y) stand for the space of all bounded linear operators between real Banach spaces X and Y, and let Σ be a σ-algebra of sets. A bounded linear operator T from the Banach space B(Σ,X) of X-valued Σ-totally measurable functions to Y is said to be σ-smooth if ‖T(fn)Y‖→0 whenever a sequence of scalar functions (‖fn(⋅)X‖) is order convergent to 0 in B(Σ). It is shown that a bounded linear operator is σ-smooth if and only if its representing measure is variationally semi-regular, i.e., as An↓∅ (here stands for the semivariation of m on A∈Σ). As an application, we show that the space Lσs(B(Σ,X),Y) of all σ-smooth operators from B(Σ,X) to Y provided with the strong operator topology is sequentially complete. We derive a Banach-Steinhaus type theorem for σ-smooth operators from B(Σ,X) to Y. Moreover, we characterize countable additivity of measures in terms of continuity of the corresponding operators . 相似文献
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B-Weyl spectrum and poles of the resolvent 总被引:1,自引:0,他引:1
M. Berkani 《Journal of Mathematical Analysis and Applications》2002,272(2):596-603
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Julie Yeramian 《Journal of Pure and Applied Algebra》2009,213(6):1013-1025
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Liangping Jiang 《Journal of Mathematical Analysis and Applications》2007,326(2):1379-1382
The classical criterion of asymptotic stability of the zero solution of equations x′=f(t,x) is that there exists a function V(t,x), a(‖x‖)?V(t,x)?b(‖x‖) for some a,b∈K, such that for some c∈K. In this paper we prove that if f(t,x) is bounded, is uniformly continuous and bounded, then the condition that can be weakened and replaced by and contains no complete trajectory of , t∈[−T,T], where , uniformly for (t,x)∈[−T,T]×BH. 相似文献
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A Roman dominating function of a graph G is a labeling f:V(G)?{0,1,2} such that every vertex with label 0 has a neighbor with label 2. The Roman domination number γR(G) of G is the minimum of ∑v∈V(G)f(v) over such functions. A Roman dominating function of G of weight γR(G) is called a γR(G)-function. A Roman dominating function f:V?{0,1,2} can be represented by the ordered partition (V0,V1,V2) of V, where Vi={v∈V∣f(v)=i}. Cockayne et al. [E.J. Cockayne, P.A. Dreyer, S.M. Hedetniemi, S.T. Hedetniemi, On Roman domination in graphs, Discrete Math. 278 (2004) 11-22] posed the following question: What can we say about the minimum and maximum values of |V0|,|V1|,|V2| for a γR-function f=(V0,V1,V2) of a graph G? In this paper we first show that for any connected graph G of order n≥3, , where γ(G) is the domination number of G. Also we prove that for any γR-function f=(V0,V1,V2) of a connected graph G of order n≥3, , and . 相似文献
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An integer matrix A∈Md(Z) induces a covering σA of Td and an endomorphism αA:f?f°σA of C(Td) for which there is a natural transfer operator L. In this paper, we compute the KMS states on the Exel crossed product C(Td)?αA,LN and its Toeplitz extension. We find that C(Td)?αA,LN has a unique KMS state, which has inverse temperature . Its Toeplitz extension, on the other hand, exhibits a phase transition at , and for larger β the simplex of KMSβ states is isomorphic to the simplex of probability measures on Td. 相似文献
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Let MC denote a 2 × 2 upper triangular operator matrix of the form , which is acting on the sum of Banach spaces X⊕Y or Hilbert spaces H⊕K. In this paper, the sets and ?C∈B(K,H)σr(MC) are, respectively, characterized completely, where σc(·) denotes the continuous spectrum, σp(·) denotes the point spectrum and σr(·) denotes the residual spectrum. Moreover, some corresponding counterexamples are given. 相似文献
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We consider a process given by the SDE , t∈[0,T), with initial condition , where T∈(0,∞], α∈R, (Bt)t∈[0,T) is a standard Wiener process, b:[0,T)→R?{0} and σ:[0,T)→(0,∞) are continuously differentiable functions. Assuming , t∈[0,T), with some K∈R, we derive an explicit formula for the joint Laplace transform of and for all t∈[0,T) and for all α∈R. Our motivation is that the maximum likelihood estimator (MLE) of α can be expressed in terms of these random variables. As an application, we show that in case of α=K, K≠0,
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Helmut Lenzing 《Linear algebra and its applications》2009,430(4):947-956
A polynomial f(T)∈Z[T] is represented by q(T)∈Z[T] if ; f(T) is graphically represented if for χM(T) the characteristic polynomial of a symmetric matrix M. Many instances of Coxeter polynomialsfA(T), for A a finite dimensional algebra, are (graphically) representable. We study the case of extended canonical algebras A, see [H. Lenzing, J.A. de la Peña, Extended canonical algebras and Fuchsian singularities, in press], show that the corresponding polynomials fA(T) are representable and satisfy a Chebysheff type recursion formula. We get consequences for the eigenvalues of the Coxeter transformation of A showing, for instance, that at most four eigenvalues may lie outside the unit circle. 相似文献
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Let X be a reduced connected k-scheme pointed at a rational point x∈X(k). By using tannakian techniques we construct the Galois closure of an essentially finite k-morphism f:Y→X satisfying the condition H0(Y,OY)=k; this Galois closure is a torsor dominating f by an X-morphism and universal for this property. Moreover, we show that is a torsor under some finite group scheme we describe. Furthermore we prove that the direct image of an essentially finite vector bundle over Y is still an essentially finite vector bundle over X. We develop for torsors and essentially finite morphisms a Galois correspondence similar to the usual one. As an application we show that for any pointed torsor f:Y→X under a finite group scheme satisfying the condition H0(Y,OY)=k, Y has a fundamental group scheme π1(Y,y) fitting in a short exact sequence with π1(X,x). 相似文献
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This paper studies a variation of domination in graphs called rainbow domination. For a positive integer k, a k-rainbow dominating function of a graph G is a function f from V(G) to the set of all subsets of {1,2,…,k} such that for any vertex v with f(v)=0? we have ∪u∈NG(v)f(u)={1,2,…,k}. The 1-rainbow domination is the same as the ordinary domination. The k-rainbow domination problem is to determine the k-rainbow domination number of a graph G, that is the minimum value of ∑v∈V(G)|f(v)| where f runs over all k-rainbow dominating functions of G. In this paper, we prove that the k-rainbow domination problem is NP-complete even when restricted to chordal graphs or bipartite graphs. We then give a linear-time algorithm for the k-rainbow domination problem on trees. For a given tree T, we also determine the smallest k such that . 相似文献
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Charles J.K. Batty 《Journal of Differential Equations》2003,194(2):300-327
The non-analytic growth bound ζ(T) of a C0-semigroup T measures the extent to which T can be approximated by a holomorphic function, and it is related to spectral properties of the generator A in regions of far from the real axis. We show that ζ(T) can be characterised by means of Fourier multiplier properties of the resolvent of A far from the real axis, and also by existence and uniqueness of mild solutions of inhomogeneous Cauchy problems of the form u′(t)=Au(t)+f(t) on where the Carleman spectra of f and u are far from the origin. The corresponding results for the exponential growth bound ω0(T) have been established earlier by other authors. 相似文献
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Let T and A be two nonnegative regular summability matrices and W(T,p)∩l∞ and cA(b) denote the spaces of all bounded strongly T-summable sequences with index p>0, and bounded summability domain of A, respectively. In this paper we show, among other things, that is a multiplier from W(T,p)∩l∞ into cA(b) if and only if any subset K of positive integers that has T-density zero implies that K has A-density zero. These results are used to characterize the A-statistical comparisons for both bounded as well as arbitrary sequences. Using the concept of A-statistical Tauberian rate, we also show that is not a multiplier from W(T,p)∩l∞ into cA(b) that leads to a Steinhaus type result. 相似文献
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Let Δ(T) and μ(T) denote the maximum degree and the Laplacian spectral radius of a tree T, respectively. Let Tn be the set of trees on n vertices, and . In this paper, we determine the two trees which take the first two largest values of μ(T) of the trees T in when . And among the trees in , the tree which alone minimizes the Laplacian spectral radius is characterized. We also prove that for two trees T1 and T2 in , if Δ(T1)>Δ(T2) and , then μ(T1)>μ(T2). As an application of these results, we give a general approach about extending the known ordering of trees in Tn by their Laplacian spectral radii. 相似文献
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Hungyung Chang 《Discrete Mathematics》2009,309(10):3185-3196
Let f be a graph function which assigns to each graph H a non-negative integer f(H)≤|V(H)|. The f-game chromatic number of a graph G is defined through a two-person game. Let X be a set of colours. Two players, Alice and Bob, take turns colouring the vertices of G with colours from X. A partial colouring c of G is legal (with respect to graph function f) if for any subgraph H of G, the sum of the number of colours used in H and the number of uncoloured vertices of H is at least f(H). Both Alice and Bob must colour legally (i.e., the partial colouring produced needs to be legal). The game ends if either all the vertices are coloured or there are uncoloured vertices with no legal colour. In the former case, Alice wins the game. In the latter case, Bob wins the game. The f-game chromatic number of G, χg(f,G), is the least number of colours that the colour set X needs to contain so that Alice has a winning strategy. Let be the graph function defined as , for any n≥3 and otherwise. Then is called the acyclic game chromatic number of G. In this paper, we prove that any outerplanar graph G has acyclic game chromatic number at most 7. For any integer k, let ?k be the graph function defined as ?k(K2)=2 and ?k(Pk)=3 (Pk is the path on k vertices) and ?k(H)=0 otherwise. This paper proves that if k≥8 then for any tree T, χg(?k,T)≤9. On the other hand, if k≤6, then for any integer n, there is a tree T such that χg(?k,T)≥n. 相似文献