共查询到20条相似文献,搜索用时 15 毫秒
1.
Huajun Huang 《Linear algebra and its applications》2010,432(12):3250-3257
We extend, in the context of connected noncompact semisimple Lie group, two results of Antezana, Massey, and Stojanoff: Given 0<λ<1, (a) the limit points of the sequence are normal, and (b) , where ‖X‖ is the spectral norm and r(X) is the spectral radius of X∈Cn×n and Δλ(X) is the λ-Aluthge transform of X. 相似文献
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Let A(λ) be a complex regular matrix polynomial of degree ? with g elementary divisors corresponding to the finite eigenvalue λ0. We show that for most complex matrix polynomials B(λ) with degree at most ? satisfying rank the perturbed polynomial (A+B)(λ) has exactly elementary divisors corresponding to λ0, and we determine their degrees. If does not exceed the number of λ0-elementary divisors of A(λ) with degree greater than 1, then the λ0-elementary divisors of (A+B)(λ) are the elementary divisors of A(λ) corresponding to λ0 with smallest degree, together with rank(B(λ)-B(λ0)) linear λ0-elementary divisors. Otherwise, the degree of all the λ0-elementary divisors of (A+B)(λ) is one. This behavior happens for any matrix polynomial B(λ) except those in a proper algebraic submanifold in the set of matrix polynomials of degree at most ?. If A(λ) has an infinite eigenvalue, the corresponding result follows from considering the zero eigenvalue of the perturbed dual polynomial. 相似文献
3.
Václav Vlasák 《Topology and its Applications》2008,155(15):1672-1676
We investigate connections between complexity of a function f from a Polish space X to a Polish space Y and complexity of the set , where K(X) denotes the space of all compact subsets of X equipped with the Vietoris topology. We prove that if C(f) is analytic, then f is Borel; and assuming -determinacy we show that f is Borel if and only if C(f) is coanalytic. Similar results for projective classes are also presented. 相似文献
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The notion of a modular is introduced as follows. A (metric) modular on a set X is a function w:(0,∞)×X×X→[0,∞] satisfying, for all x,y,z∈X, the following three properties: x=y if and only if w(λ,x,y)=0 for all λ>0; w(λ,x,y)=w(λ,y,x) for all λ>0; w(λ+μ,x,y)≤w(λ,x,z)+w(μ,y,z) for all λ,μ>0. We show that, given x0∈X, the set Xw={x∈X:limλ→∞w(λ,x,x0)=0} is a metric space with metric , called a modular space. The modular w is said to be convex if (λ,x,y)?λw(λ,x,y) is also a modular on X. In this case Xw coincides with the set of all x∈X such that w(λ,x,x0)<∞ for some λ=λ(x)>0 and is metrizable by . Moreover, if or , then ; otherwise, the reverse inequalities hold. We develop the theory of metric spaces, generated by modulars, and extend the results by H. Nakano, J. Musielak, W. Orlicz, Ph. Turpin and others for modulars on linear spaces. 相似文献
5.
Preservers of spectral radius, numerical radius, or spectral norm of the sum on nonnegative matrices
Chi-Kwong Li 《Linear algebra and its applications》2009,430(7):1739-1398
Let be the set of entrywise nonnegative n×n matrices. Denote by r(A) the spectral radius (Perron root) of . Characterization is obtained for maps such that r(f(A)+f(B))=r(A+B) for all . In particular, it is shown that such a map has the form
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For a metric continuum X, we consider the hyperspaces X2 and C(X) of the closed and nonempty subsets of X and of subcontinua of X, respectively, both with the Hausdorff metric. For a given map we investigate the transitivity of the induced maps and . Among other results, we show that if X is a dendrite or a continuum of type λ and is a map, then C(f) is not transitive. However, if X is the Hilbert cube, then there exists a transitive map such that f2 and C(f) are transitive. 相似文献
8.
Nicu?or Costea 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):4271-4278
We study the problem in Ω, u=0 on ∂Ω, where Ω is a bounded domain in RN, is a continuous function and λ and ε are two positive constants. We prove that for any ε>0 each λ∈(0,λ1) is an eigenvalue of the above problem, where λ1 is the principal eigenvalue of the Laplace operator on Ω. Moreover, for each eigenvalue λ∈(0,λ1) it corresponds a unique eigenfunction. The proofs will be based on the Banach fixed point theorem combined with adequate variational techniques. 相似文献
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For a bounded function f from the unit sphere of a closed subspace X of a Banach space Y, we study when the closed convex hull of its spatial numerical range W(f) is equal to its intrinsic numerical range V(f). We show that for every infinite-dimensional Banach space X there is a superspace Y and a bounded linear operator such that . We also show that, up to renormig, for every non-reflexive Banach space Y, one can find a closed subspace X and a bounded linear operator T∈L(X,Y) such that .Finally, we introduce a sufficient condition for the closed convex hull of the spatial numerical range to be equal to the intrinsic numerical range, which we call the Bishop-Phelps-Bollobás property, and which is weaker than the uniform smoothness and the finite-dimensionality. We characterize strong subdifferentiability and uniform smoothness in terms of this property. 相似文献
12.
Xianling Fan 《Journal of Mathematical Analysis and Applications》2009,349(2):436-442
Consider the eigenvalue problem : −Δu=λf(x,u) in Ω, u=0 on ∂Ω, where Ω is a bounded smooth domain in RN. Denote by the set of all Carathéodory functions f:Ω×R→R such that for a.e. x∈Ω, f(x,⋅) is Lipschitzian with Lipschitz constant L, f(x,0)=0 and , and denote by (resp. ) the set of λ>0 such that has at least one nonzero classical (resp. weak) solution. Let λ1 be the first eigenvalue for the Laplacian-Dirichlet problem. We prove that and . Our result is a positive answer to Ricceri's conjecture if use f(x,u) instead of f(u) in the conjecture. 相似文献
13.
M. Anoussis 《Advances in Mathematics》2004,188(2):425-443
Let G be a compact group, not necessarily abelian, let ? be its unitary dual, and for f∈L1(G), let fn?f∗?∗f denote n-fold convolution of f with itself and f? the Fourier transform of f. In this paper, we derive the following spectral radius formula
14.
Rachel Quinlan 《Linear algebra and its applications》2011,434(6):1580-2271
Let V be a vector space of dimension n over any field F. Extreme values for the possible dimension of a linear subspace of EndF(V) with a particular property are considered in two specific cases. It is shown that if E1 is a subspace of EndF(V) and there exists an endomorphism g of V, not in E1, such that for every hyperplane H of V some element of E1 agrees with g on H, then E1 has dimension at least . This answers a question that was posed by Szechtman in 2003. It is also shown that a linear subspace of Mn(F) in which no element possesses a non-zero eigenvalue in F may have dimension at most . The connection between these two properties, which arises from duality considerations, is discussed. 相似文献
15.
In the present paper, a class F of critically finite transcendental meromorphic functions having rational Schwarzian derivative is introduced and the dynamics of functions in one parameter family is investigated. It is found that there exist two parameter values λ∗=?(0)>0 and , where and is the real root of ?′(x)=0, such that the Fatou sets of fλ(z) for λ=λ∗ and λ=λ∗∗ contain parabolic domains. A computationally useful characterization of the Julia set of the function fλ(z) as the complement of the basin of attraction of an attracting real fixed point of fλ(z) is established and applied for the generation of the images of the Julia sets of fλ(z). Further, it is observed that the Julia set of fλ∈K explodes to whole complex plane for λ>λ∗∗. Finally, our results found in the present paper are compared with the recent results on dynamics of one parameter families λtanz, [R.L. Devaney, L. Keen, Dynamics of meromorphic maps: Maps with polynomial Schwarzian derivative, Ann. Sci. École Norm. Sup. 22 (4) (1989) 55-79; L. Keen, J. Kotus, Dynamics of the family λtan(z), Conform. Geom. Dynam. 1 (1997) 28-57; G.M. Stallard, The Hausdorff dimension of Julia sets of meromorphic functions, J. London Math. Soc. 49 (1994) 281-295] and , λ>0 [G.P. Kapoor, M. Guru Prem Prasad, Dynamics of : The Julia set and bifurcation, Ergodic Theory Dynam. Systems 18 (1998) 1363-1383]. 相似文献
16.
Graham Brightwell 《Discrete Mathematics》2010,310(5):1016-1025
We consider a natural analogue of the graph linear arrangement problem for posets. Let P=(X,?) be a poset that is not an antichain, and let λ:X→[n] be an order-preserving bijection, that is, a linear extension of P. For any relation a?b of P, the distance between a and b in λ is λ(b)−λ(a). The average relational distance of λ, denoted , is the average of these distances over all relations in P. We show that we can find a linear extension of P that maximises in polynomial time. Furthermore, we show that this maximum is at least , and this bound is extremal. 相似文献
17.
Dongmei Zhu 《Linear algebra and its applications》2010,432(11):2764-2772
In this paper, we obtain the following upper bound for the largest Laplacian graph eigenvalue λ(G):
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Consider the surjective, continuous map f:X→X and the continuous map of K(X) into itself induced by f, where X is a compact metric space and K(X) is the space of all non-empty compact subsets of X endowed with a Hausdorff metric. In this paper we give examples showing that sensitivity of f does not imply sensitivity of . Furthermore, we prove that if f is a surjective, continuous interval map, then is sensitive if and only if f is sensitive. 相似文献
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A.V. Ivanov 《Topology and its Applications》2010,157(3):517-521
We construct, assuming the continuum hypothesis, an example of nonmetrizable n-dimensional Cantor manifold Xn(n∈N) with the following properties: 1) is hereditarily separable for all k∈N; 2) is perfectly normal for every k∈N; 3) the space F(Xn) is hereditarily normal for every seminormal functor F that preserves weights and one-to-one points and such that sp(F)={1,k}; in particular, and λ3Xn are hereditarily normal. This example is a generalization of famous Gruenhage's example given in Gruenhage and Nyikos (1993) [4]. 相似文献