共查询到20条相似文献,搜索用时 31 毫秒
1.
Sen-Zhong Huang 《Semigroup Forum》1999,58(3):323-335
Let {e tA: t ≥ 0} be a C0—semigroup on the Hilbert space ?. If x 0 ∈ ? is such that the local resolvent R(λ,A) x 0 admits a bounded holomorphic extension to the open half plane {Reλ > 0}, then lim t→∞‖e tA R(λ0, A) x 0‖ = 0 for each λ0 ∈ ρ(A). This resuit is used to find mild spectral conditions which ensure the decay at infmity to zero of solutions of higher order abstract Cauchy problems. 相似文献
2.
We consider products of unitary operators with at most two points in their spectra, 1 and eiα. We prove that the scalar operator eiγI is a product of k such operators if α(1+1/(k-3))?γ?α(k-1-1/(k-3)) for k?5. Also we prove that for eiα≠-1, only a countable number of scalar operators can be decomposed in a product of four operators from the mentioned class. As a corollary we show that every unitary operator on an infinite-dimensional space is a product of finitely many such operators. 相似文献
3.
Mustapha Mokhtar-Kharroubi 《Journal of Evolution Equations》2008,8(2):327-352
We deal with streaming operators T
H
defined in L
1 spaces by the directional derivative with positive boundary operator H of norm 1 relating the incoming and outgoing fluxes. It is known that T
H
need not be a generator but there exists a contraction semigroup generated by an extension A of T
H
. This paper deals with the total mass carried by individual trajectories {e
tA
f; t ≥ 0} for nonnegative initial data f and related topics. In particular, our analysis covers the problem of (the lack of) stochasticity of {e
tA
; t ≥ 0} for conservative boundary operator H.
相似文献
4.
Given a family (etAk)t0(k
) of commuting contraction semigroups, we investigate when the infinite product ∏∞k=1 etAkconverges and defines aC0-semigroup. A particular case is the heat semigroup in infinite dimension introduced by Cannarsa and Da Prato (J. Funct. Anal.118(1993), 22–42). 相似文献
6.
Mihály Weiner 《Linear algebra and its applications》2010,433(3):520-533
In this work it is shown that certain interesting types of orthogonal system of subalgebras (whose existence cannot be ruled out by the trivial necessary conditions) cannot exist. In particular, it is proved that there is no orthogonal decomposition of Mn(C)⊗Mn(C)≡Mn2(C) into a number of maximal abelian subalgebras and factors isomorphic to Mn(C) in which the number of factors would be 1 or 3.In addition, some new tools are introduced, too: for example, a quantity c(A,B), which measures “how close” the subalgebras A,B⊂Mn(C) are to being orthogonal. It is shown that in the main cases of interest, c(A′,B′) - where A′ and B′ are the commutants of A and B, respectively - can be determined by c(A,B) and the dimensions of A and B. The corresponding formula is used to find some further obstructions regarding orthogonal systems. 相似文献
7.
A.R. Ashrafi M. SaheliM. Ghorbani 《Journal of Computational and Applied Mathematics》2011,235(16):4561-4566
Let G be a molecular graph. The eccentric connectivity index ξc(G) is defined as ξc(G)=∑u∈V(G)degG(u)εG(u), where degG(u) denotes the degree of vertex u and εG(u) is the largest distance between u and any other vertex v of G. In this paper exact formulas for the eccentric connectivity index of TUC4C8(S) nanotube and TC4C8(S) nanotorus are given. 相似文献
8.
In this paper, we reconsider the iterative method Xk=Xk−1+βY(I−AXk−1), k=1,2,…,β∈C?{0} for computing the generalized inverse over Banach spaces or the generalized Drazin inverse ad of a Banach algebra element a, reveal the intrinsic relationship between the convergence of such iterations and the existence of or ad, and present the error bounds of the iterative methods for approximating or ad. Moreover, we deduce some necessary and sufficient conditions for iterative convergence to or ad. 相似文献
9.
10.
Fred B Weissler 《Journal of Functional Analysis》1979,32(3):277-296
We study the evolution equation u′(t) = Au(t) + J(u(t)), t ? 0, where etA is a C0 semi-group on a Banach space E, and J is a “singular” non-linear mapping defined on a subset of E. In Sections 1 and 2 of the paper we suppress the map J and instead consider maps Kt: E → E, t > 0, which heuristically are just etAJ. Under certain integrability conditions on the Kt we prove existence and uniqueness of local solutions to the integral equation u(t) = etAφ + ∝0tKt ? s(u(s)) ds for all φ in E, and investigate the regularity of the solutions. Conditions which insure existence of global solutions are given. In Section 3 we recover the map J from the maps Kt, and show that the generator of the semi-flow on E induced by the integral equation has dense domain. Finally, we apply these results to a large class of examples which includes polynomial perturbations to elliptic operators on a domain in Rn. 相似文献
11.
12.
The main purpose of this paper is to study the continuity of several kinds of generalized inverses of elements in a Banach algebra with identity. We first obtain a sufficient and necessary condition for the lower semi-continuity of reflexive generalized inverses as set-valued mappings. Based on this result, we characterize the continuity of the Moore-Penrose inverse in a C∗-algebra and therefore, derive some new and well-known criteria in operator theory. 相似文献
13.
Masayoshi Kaneda 《Journal of Functional Analysis》2007,251(1):346-359
Let X be an operator space, let φ be a product on X, and let (X,φ) denote the algebra that one obtains. We give necessary and sufficient conditions on the bilinear mapping φ for the algebra (X,φ) to have a completely isometric representation as an algebra of operators on some Hilbert space. In particular, we give an elegant geometrical characterization of such products by using the Haagerup tensor product. Our result makes no assumptions about identities or approximate identities. Our proof is independent of the earlier result of Blecher, Ruan and Sinclair [D.P. Blecher, Z.-J. Ruan, A.M. Sinclair, A characterization of operator algebras, J. Funct. Anal. 89 (1) (1990) 188-201] which solved the case when the bilinear mapping has an identity of norm one, and our result is used to give a simple direct proof of this earlier result. We also develop further the connections between quasi-multipliers of operator spaces and their representations on a Hilbert space or their embeddings in the second dual, and show that the quasi-multipliers of operator spaces defined in [M. Kaneda, V.I. Paulsen, Quasi-multipliers of operator spaces, J. Funct. Anal. 217 (2) (2004) 347-365] coincide with their C∗-algebraic counterparts. 相似文献
14.
Suppose G is a graph and λ1,λ2,…,λn are the eigenvalues of G. The Estrada index EE(G) of G is defined as the sum of eλi, 1≤i≤n. In this paper some new upper bounds for the Estrada index of bipartite graphs are presented. We apply our result on a (4,6)-fullerene to improve our bound given in an earlier paper. 相似文献
15.
Let H be a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. An operator A in L(H) is said to be a Cowen-Douglas operator if there exist Ω, a connected open subset of complex plane C, and n, a positive integer, such that
- (a)
- (b)
- for z in Ω;
- (c)
- ; and
- (d)
- for z in Ω.
16.
Let Mn(F) denote the algebra of n×n matrices over the field F of complex, or real, numbers. Given a self-adjoint involution J∈Mn(C), that is, J=J*,J2=I, let us consider Cn endowed with the indefinite inner product [,] induced by J and defined by [x,y]?〈Jx,y〉,x,y∈Cn. Assuming that (r,n-r), 0?r?n, is the inertia of J, without loss of generality we may assume J=diag(j1,?,jn)=Ir⊕-In-r. For T=(|tik|2)∈Mn(R), the matrices of the form T=(|tik|2jijk), with all line sums equal to 1, are called J-doubly stochastic matrices. In the particular case r∈{0,n}, these matrices reduce to doubly stochastic matrices, that is, non-negative real matrices with all line sums equal to 1. A generalization of Birkhoff’s theorem on doubly stochastic matrices is obtained for J-doubly stochastic matrices and an application to determinants is presented. 相似文献
17.
We give an interpolation-free proof of the known fact that a dyadic paraproduct is of Schatten-von Neumann class Sp, if and only if its symbol is in the dyadic Besov space Bpd. Our main tools are a product formula for paraproducts and a “p-John-Nirenberg-Theorem” due to Rochberg and Semmes.We use the same technique to prove a corresponding result for dyadic paraproducts with operator symbols.Using an averaging technique by Petermichl, we retrieve Peller's characterizations of scalar and vector Hankel operators of Schatten-von Neumann class Sp for 1<p<∞. We then employ vector techniques to characterise little Hankel operators of Schatten-von Neumann class, answering a question by Bonami and Peloso.Furthermore, using a bilinear version of our product formula, we obtain characterizations for boundedness, compactness and Schatten class membership of products of dyadic paraproducts. 相似文献
18.
Jason R. Morris 《Journal of Differential Equations》2006,225(2):573-604
Given a piecewise continuous function and a projection P1 onto a subspace X1 of CN, we investigate the injectivity, surjectivity and, more generally, the Fredholm properties of the ordinary differential operator with boundary condition . This operator acts from the “natural” space into L2×X1. A main novelty is that it is not assumed that A is bounded or that has any dichotomy, except to discuss the impact of the results on this special case. We show that all the functional properties of interest, including the characterization of the Fredholm index, can be related to the existence of a selfadjoint solution H of the Riccati differential inequality . Special attention is given to the simple case when H=A+A∗ satisfies this inequality. When H is known, all the other hypotheses and criteria are easily verifiable in most concrete problems. 相似文献
19.
Mouez Dimassi 《Journal of Functional Analysis》2003,198(1):142-159
We give a local trace formula for the pair (P1(h)=P0+W(hy),P0), where P0 is a periodic Schrödinger operator, W is a decreasing perturbation and h is a small positive parameter. We apply this result to establish the existence of ∼h−n resonances near some energy λ of σ(P0). 相似文献
20.
The hypersurfaces of degree d in the projective space Pn correspond to points of PN, where . Now assume d=2e is even, and let X(n,d)⊆PN denote the subvariety of two e-fold hyperplanes. We exhibit an upper bound on the Castelnuovo regularity of the ideal of X(n,d), and show that this variety is r-normal for r?2. The latter result is representation-theoretic, and says that a certain GLn+1-equivariant morphism
Sr(S2e(Cn+1))→S2(Sre(Cn+1)) 相似文献