共查询到20条相似文献,搜索用时 656 毫秒
1.
Wolfgang Arendt 《Journal of Functional Analysis》2006,238(1):340-352
Let A be the generator of a cosine function on a Banach space X. In many cases, for example if X is a UMD-space, A+B generates a cosine function for each B∈L(D((ω−A)1/2),X). If A is unbounded and , then we show that there exists a rank-1 operator B∈L(D(γ(ω−A)),X) such that A+B does not generate a cosine function. The proof depends on a modification of a Baire argument due to Desch and Schappacher. It also allows us to prove the following. If A+B generates a distribution semigroup for each operator B∈L(D(A),X) of rank-1, then A generates a holomorphic C0-semigroup. If A+B generates a C0-semigroup for each operator B∈L(D(γ(ω−A)),X) of rank-1 where 0<γ<1, then the semigroup T generated by A is differentiable and ‖T′(t)‖=O(t−α) as t↓0 for any α>1/γ. This is an approximate converse of a perturbation theorem for this class of semigroups. 相似文献
2.
Shuzhou Wang 《Journal of Functional Analysis》2009,256(10):3313-3341
The notion of simple compact quantum group is introduced. As non-trivial (noncommutative and noncocommutative) examples, the following families of compact quantum groups are shown to be simple: (a) The universal quantum groups Bu(Q) for Q∈GL(n,C) satisfying , n?2; (b) The quantum automorphism groups Aaut(B,τ) of finite-dimensional C∗-algebras B endowed with the canonical trace τ when dim(B)?4, including the quantum permutation groups Aaut(Xn) on n points (n?4); (c) The standard deformations Kq of simple compact Lie groups K and their twists , as well as Rieffel's deformation KJ. 相似文献
3.
When A∈B(H) and B∈B(K) are given, we denote by MC the operator acting on the infinite-dimensional separable Hilbert space H⊕K of the form . In this paper, it is shown that there exists some operator C∈B(K,H) such that MC is upper semi-Fredholm and ind(MC)?0 if and only if there exists some left invertible operator C∈B(K,H) such that MC is upper semi-Fredholm and ind(MC)?0. A necessary and sufficient condition for MC to be upper semi-Fredholm and ind(MC)?0 for some C∈Inv(K,H) is given, where Inv(K,H) denotes the set of all the invertible operators of B(K,H). In addition, we give a necessary and sufficient condition for MC to be upper semi-Fredholm and ind(MC)?0 for all C∈Inv(K,H). 相似文献
4.
Dhruba R. Adhikari 《Journal of Mathematical Analysis and Applications》2008,348(1):122-136
Let X be a real reflexive Banach space with dual X∗. Let L:X⊃D(L)→X∗ be densely defined, linear and maximal monotone. Let T:X⊃D(T)→X∗2, with 0∈D(T) and 0∈T(0), be strongly quasibounded and maximal monotone, and C:X⊃D(C)→X∗ bounded, demicontinuous and of type (S+) w.r.t. D(L). A new topological degree theory has been developed for the sum L+T+C. This degree theory is an extension of the Berkovits-Mustonen theory (for T=0) and an improvement of the work of Addou and Mermri (for T:X→X∗2 bounded). Unbounded maximal monotone operators with are strongly quasibounded and may be used with the new degree theory. 相似文献
5.
Rafa? Kapica Janusz Morawiec 《Applied mathematics and computation》2011,217(21):8311-8317
Taking advantage of perpetuities and the asymptotic behavior of products of random matrices we obtain the direct form of the Fourier transform of an L1-solution of the following random matrix refinement type equation
f(x)=∫Ω|detL(ω)|C(ω)f(L(ω)x-M(ω))P(dω), 相似文献
6.
For a measurable space (Ω,A), let ?∞(A) be the closure of span{χA:A∈A} in ?∞(Ω). In this paper we show that a sufficient and necessary condition for a real-valued finitely additive measure μ on (Ω,A) to be countably additive is that the corresponding functional ?μ defined by (for x∈?∞(A)) is w*-sequentially continuous. With help of the Yosida-Hewitt decomposition theorem of finitely additive measures, we show consequently that every continuous functional on ?∞(A) can be uniquely decomposed into the ?1-sum of a w*-continuous functional, a purely w*-sequentially continuous functional and a purely (strongly) continuous functional. Moreover, several applications of the results to measure extension are given. 相似文献
7.
Suppose T is a bounded self-adjoint operator on the Hilbert space L2(X,μ) and let
8.
Mathias Beiglböck 《Journal of Number Theory》2007,127(2):145-152
András Biró and Vera Sós prove that for any subgroup G of T generated freely by finitely many generators there is a sequence A⊆N such that for all β∈T we have (‖.‖ denotes the distance to the nearest integer)
9.
Julio Becerra Guerrero Fernando Rambla-Barreno 《Journal of Mathematical Analysis and Applications》2009,360(1):254-264
We prove that for every member X in the class of real or complex JB*-triples or preduals of JBW*-triples, the following assertions are equivalent:
- (1) X has the fixed point property.
- (2) X has the super fixed point property.
- (3) X has normal structure.
- (4) X has uniform normal structure.
- (5) The Banach space of X is reflexive.
Keywords: JB*-triple; Fixed point; Normal structure 相似文献
10.
Manwai Yuen 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(4):1465-1470
In this paper, we study the blowup of the N-dim Euler or Euler-Poisson equations with repulsive forces, in radial symmetry. We provide a novel integration method to show that the non-trivial classical solutions (ρ,V), with compact support in [0,R], where R>0 is a positive constant and in the sense which ρ(t,r)=0 and V(t,r)=0 for r≥R, under the initial condition
(1) 相似文献
11.
Vladimir Nikiforov 《Journal of Mathematical Analysis and Applications》2008,337(1):739-743
Let A be an n×n complex matrix and r be the maximum size of its principal submatrices with no off-diagonal zero entries. Suppose A has zero main diagonal and x is a unit n-vector. Then, letting ‖A‖ be the Frobenius norm of A, we show that
|〈Ax,x〉|2?(1−1/2r−1/2n)‖A‖2. 相似文献
12.
Chi-Wai Leung 《Journal of Mathematical Analysis and Applications》2006,322(2):699-711
In this article, we define a natural Banach ∗-algebra for a C∗-dynamical system (A,G,α) which is slightly bigger than L1(G;A) (they are the same if A is finite-dimensional). We will show that this algebra is ∗-regular if G has polynomial growth. The main result in this article extends the two main results in [C.W. Leung, C.K. Ng, Functional calculus and ∗-regularity of a class of Banach algebras, Proc. Amer. Math. Soc., in press]. 相似文献
13.
P. Kasprzak 《Journal of Functional Analysis》2009,257(5):1288-163
14.
Jung-Rye Lee 《Journal of Mathematical Analysis and Applications》2008,339(1):372-383
Let X and Y be Banach spaces and f:X→Y an odd mapping. We solve the following generalized additive functional equation
15.
Ming-Yi Lee Chin-Cheng Lin Ying-Chieh Lin 《Journal of Mathematical Analysis and Applications》2008,348(2):787-796
Let K be a generalized Calderón-Zygmund kernel defined on Rn×(Rn?{0}). The singular integral operator with variable kernel given by
16.
Bertrand Lemaire 《Discrete Mathematics》2006,306(15):1669-1683
We give a characterization of the non-empty binary relations ? on a N*-set A such that there exist two morphisms of N*-sets u1,u2:A→R+ verifying u1?u2 and x?y⇔u1(x)>u2(y). They are called homothetic interval orders. If ? is a homothetic interval order, we also give a representation of ? in terms of one morphism of N*-sets u:A→R+ and a map such that x?y⇔σ(x,y)u(x)>u(y). The pairs (u1,u2) and (u,σ) are “uniquely” determined by ?, which allows us to recover one from each other. We prove that ? is a semiorder (resp. a weak order) if and only if σ is a constant map (resp. σ=1). If moreover A is endowed with a structure of commutative semigroup, we give a characterization of the homothetic interval orders ? represented by a pair (u,σ) so that u is a morphism of semigroups. 相似文献
17.
Mohamed Aziz Taoudi 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):478-3452
In this paper we prove the following Krasnosel’skii type fixed point theorem: Let M be a nonempty bounded closed convex subset of a Banach space X. Suppose that A:M→X and B:X→X are two weakly sequentially continuous mappings satisfying:
- (i)
- AM is relatively weakly compact;
- (ii)
- B is a strict contraction;
- (iii)
- .
18.
Given a graph G, for an integer c∈{2,…,|V(G)|}, define λc(G)=min{|X|:X⊆E(G),ω(G−X)≥c}. For a graph G and for an integer c=1,2,…,|V(G)|−1, define,
19.
Yoshiharu Kohayakawa Vojtěch Rödl Mathias Schacht Papa Sissokho 《Journal of Combinatorial Theory, Series A》2007,114(4):631-657
The generalized Turán number ex(G,H) of two graphs G and H is the maximum number of edges in a subgraph of G not containing H. When G is the complete graph Km on m vertices, the value of ex(Km,H) is , where o(1)→0 as m→∞, by the Erd?s-Stone-Simonovits theorem.In this paper we give an analogous result for triangle-free graphs H and pseudo-random graphs G. Our concept of pseudo-randomness is inspired by the jumbled graphs introduced by Thomason [A. Thomason, Pseudorandom graphs, in: Random Graphs '85, Poznań, 1985, North-Holland, Amsterdam, 1987, pp. 307-331. MR 89d:05158]. A graph G is (q,β)-bi-jumbled if
20.
K.V. Storozhuk 《Journal of Mathematical Analysis and Applications》2007,332(2):1365-1370
If (Tt)t?0 is a bounded C0-semigroup in a Banach space X and there exists a compact subset K⊆X such that