共查询到20条相似文献,搜索用时 31 毫秒
1.
Stanislav Shkarin 《Journal of Functional Analysis》2010,258(1):132-160
We treat the question of existence of common hypercyclic vectors for families of continuous linear operators. It is shown that for any continuous linear operator T on a complex Fréchet space X and a set Λ⊆R+×C which is not of zero three-dimensional Lebesgue measure, the family has no common hypercyclic vectors. This allows to answer negatively questions raised by Godefroy and Shapiro and by Aron. We also prove a sufficient condition for a family of scalar multiples of a given operator on a complex Fréchet space to have a common hypercyclic vector. It allows to show that if and φ∈H∞(D) is non-constant, then the family has a common hypercyclic vector, where Mφ:H2(D)→H2(D), Mφf=φf, and , providing an affirmative answer to a question by Bayart and Grivaux. Finally, extending a result of Costakis and Sambarino, we prove that the family has a common hypercyclic vector, where Tbf(z)=f(z−b) acts on the Fréchet space H(C) of entire functions on one complex variable. 相似文献
2.
Stevo Stevi? 《Applied mathematics and computation》2010,215(11):3950-1448
The boundedness of the composition operator Cφf(z)=f(φ(z)) from the Hardy space , where X is the upper half-plane or the unit disk D={z∈C:|z|<1} in the complex plane C, to the nth weighted-type space, where φ is an analytic self-map of X, is characterized. 相似文献
3.
Xiangling Zhu 《Applied mathematics and computation》2010,215(12):4340-4972
Let H(D) denote the class of all analytic functions on the open unit disk D of C. Let φ be an analytic self-map of D and u∈H(D). The weighted composition operator is defined by
4.
Let H?1 be a selfadjoint operator in H, let J be a linear and bounded operator from (D(H1/2),∥H1/2·∥) to Haux and for β>0 let be the nonnegative selfadjoint operator in H satisfying
5.
Andrea Posilicano 《Journal of Functional Analysis》2005,223(2):259-310
Given, on the Hilbert space H0, the self-adjoint operator B and the skew-adjoint operators C1 and C2, we consider, on the Hilbert space H?D(B)⊕H0, the skew-adjoint operator
6.
On an integral-type operator from iterated logarithmic Bloch spaces into Bloch-type spaces 总被引:1,自引:0,他引:1
Let H(B) denote the space of all holomorphic functions on the open unit ball B of Cn. Let φ=(φ1,…,φn) be a holomorphic self-map of B and g∈H(B) such that g(0)=0. In this paper we study the boundedness and compactness of the following integral-type operator, recently introduced by Xiangling Zhu and the second author
7.
Li-Ping Huang 《Linear algebra and its applications》2010,433(1):221-232
Denote by G=(V,∼) a graph which V is the vertex set and ∼ is an adjacency relation on a subset of V×V. In this paper, the good distance graph is defined. Let (V,∼) and (V′,∼′) be two good distance graphs, and φ:V→V′ be a map. The following theorem is proved: φ is a graph isomorphism ⇔φ is a bounded distance preserving surjective map in both directions ⇔φ is a distance k preserving surjective map in both directions (where k<diam(G)/2 is a positive integer), etc. Let D be a division ring with an involution such that both |F∩ZD|?3 and D is not a field of characteristic 2 with D=F, where and ZD is the center of D. Let Hn(n?2) be the set of n×n Hermitian matrices over D. It is proved that (Hn,∼) is a good distance graph, where A∼B⇔rank(A-B)=1 for all A,B∈Hn. 相似文献
8.
We study the critical set C of the nonlinear differential operator F(u)=−u″+f(u) defined on a Sobolev space of periodic functions Hp(S1), p?1. Let be the plane z=0 and, for n>0, let n be the cone x2+y2=tan2z, |z−2πn|<π/2; also set . For a generic smooth nonlinearity f:R→R with surjective derivative, we show that there is a diffeomorphism between the pairs (Hp(S1),C) and (R3,Σ)×H where H is a real separable infinite-dimensional Hilbert space. 相似文献
9.
10.
Stevo Stevi? 《Applied mathematics and computation》2010,216(1):187-10194
Let D be a bounded symmetric domain, H(D) the class of all holomorphic functions on D and u∈H(D). Operator norm of the multiplication operator on the weighted Bergman space , as well as of weighted composition operator from to a weighted-type space are calculated. 相似文献
11.
12.
W.A. Kirk 《Journal of Mathematical Analysis and Applications》2003,277(2):645-650
Let be a contractive gauge function in the sense that φ is continuous, φ(s)<s for s>0, and if f:M→M satisfies d(f(x),f(y))?φ(d(x,y)) for all x,y in a complete metric space (M,d), then f always has a unique fixed point. It is proved that if T:M→M satisfies
13.
Let fr(n) be the maximum number of edges in an r-uniform hypergraph on n vertices that does not contain four distinct edges A, B, C, D with A∪B=C∪D and A∩B=C∩D=∅. This problem was stated by Erd?s [P. Erd?s, Problems and results in combinatorial analysis, Congr. Numer. 19 (1977) 3-12]. It can be viewed as a generalization of the Turán problem for the 4-cycle to hypergraphs.Let . Füredi [Z. Füredi, Hypergraphs in which all disjoint pairs have distinct unions, Combinatorica 4 (1984) 161-168] observed that ?r?1 and conjectured that this is equality for every r?3. The best known upper bound ?r?3 was proved by Mubayi and Verstraëte [D. Mubayi, J. Verstraëte, A hypergraph extension of the bipartite Turán problem, J. Combin. Theory Ser. A 106 (2004) 237-253]. Here we improve this bound. Namely, we show that for every r?3, and ?3?13/9. In particular, it follows that ?r→1 as r→∞. 相似文献
14.
Bebe Prunaru 《Journal of Functional Analysis》2008,254(6):1626-1641
Let H be a complex Hilbert space and let {Tn}n?1 be a sequence of commuting bounded operators on H such that . Let denote the space of all operators X in B(H) for which and suppose that . We will show that there exists a triple {K,Γ,{Un}n?1} where K is a Hilbert space, Γ:K→H is a bounded operator and {Un}n?1⊂B(K) is a sequence of commuting normal operators with such that TnΓ=ΓUn for n?1, and for which the mapping Y?ΓYΓ∗ is a complete isometry from the commutant of {Un}n?1 onto the space . Moreover we show that the inverse of this mapping can be extended to a ∗-homomorphism
15.
Let H2(D2) be the Hardy space over the bidisk. For sequences of Blaschke products {φn(z):−∞<n<∞} and {ψn(w):−∞<n<∞} satisfying some additional conditions, we may define a Rudin type invariant subspace M. We shall determine the rank of H2(D2)?M for the pair of operators and . 相似文献
16.
Stevo Stevi? 《Applied mathematics and computation》2009,211(1):222-233
Motivated by the recent paper [X. Zhu, Products of differentiation composition and multiplication from Bergman type spaces to Bers spaces, Integral Transform. Spec. Funct. 18 (3) (2007) 223-231], we study the boundedness and compactness of the weighted differentiation composition operator , where u is a holomorphic function on the unit disk D, φ is a holomorphic self-map of D and n∈N0, from the mixed-norm space H(p, q, ?), where p,q > 0 and ? is normal, to the weighted-type space or the little weighted-type space . For the case of the weighted Bergman space , p > 1, some bounds for the essential norm of the operator are also given. 相似文献
17.
Xiaosong Liu 《Journal of Mathematical Analysis and Applications》2006,324(1):604-614
Suppose f is a spirallike function of type β (or starlike function of order α) on the unit disk D in C. Let , where 1?p1?2 (or 0<p1?2), pj?1, j=2,…,n, are real numbers. In this paper, we prove that
18.
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
19.
Caixing Gu 《Journal of Functional Analysis》2004,215(1):178-205
Let X be a bounded linear operator on the Hardy space H2 of the unit disk. We show that if is of finite rank for every inner function θ, then X=T?+F for some Toeplitz operator T? and some finite rank operator F on H2. This solves a variant of an open question where the compactness replaces the finite rank conditions. 相似文献
20.
Let H be a Hilbert space and C be a nonempty closed convex subset of H, {Ti}i∈N be a family of nonexpansive mappings from C into H, Gi:C×C→R be a finite family of equilibrium functions (i∈{1,2,…,K}), A be a strongly positive bounded linear operator with a coefficient and -Lipschitzian, relaxed (μ,ν)-cocoercive map of C into H. Moreover, let , {αn} satisfy appropriate conditions and ; we introduce an explicit scheme which defines a suitable sequence as follows: