共查询到20条相似文献,搜索用时 687 毫秒
1.
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
2.
Michael Stoll 《Journal of Number Theory》2002,93(2):183-206
3.
4.
Let A=(A1,…,Am) be a sequence of finite subsets from an additive abelian group G. Let Σ?(A) denote the set of all group elements representable as a sum of ? elements from distinct terms of A, and set . Our main theorem is the following lower bound:
5.
Mark M. Malamud 《Journal of Functional Analysis》2011,260(3):613-638
The classical Weyl-von Neumann theorem states that for any self-adjoint operator A0 in a separable Hilbert space H there exists a (non-unique) Hilbert-Schmidt operator C=C? such that the perturbed operator A0+C has purely point spectrum. We are interesting whether this result remains valid for non-additive perturbations by considering the set ExtA of self-adjoint extensions of a given densely defined symmetric operator A in H and some fixed . We show that the ac-parts and of and A0 are unitarily equivalent provided that the resolvent difference is compact and the Weyl function M(⋅) of the pair {A,A0} admits weak boundary limits M(t):=w-limy→+0M(t+iy) for a.e. t∈R. This result generalizes the classical Kato-Rosenblum theorem. Moreover, it demonstrates that for such pairs {A,A0} the Weyl-von Neumann theorem is in general not true in the class ExtA. 相似文献
6.
7.
Ioannis A. Polyrakis 《Journal of Mathematical Analysis and Applications》2004,289(1):126-142
In this article we suppose that (Ω,Σ,μ) is a measure space and T an one-to-one, linear, continuous operator of L1(μ) into the dual E′ of a Banach space E. For any measurable set A consider the image T(L+1(μA)) of the positive cone of the space L1(μA) in E′, where μA is the restriction of the measure μ on A. We provide geometrical conditions on the cones T(L+1(μA)) which yield that the measure μ is atomic, i.e., that L1(μ) is lattice isometric to , where denotes the set of atoms of μ. This result yields also a new characterization of c0(Γ). 相似文献
8.
In this paper we investigate discrete spectrum of the non-selfadjoint matrix Sturm-Liouville operator L generated in L2(R+,S) by the differential expression
9.
Mao-Ting Chien Hiroshi Nakazato 《Journal of Mathematical Analysis and Applications》2011,373(1):297-304
Let r be a real number and A a tridiagonal operator defined by Aej=ej−1+rjej+1, j=1,2,…, where {e1,e2,…} is the standard orthonormal basis for ?2(N). Such tridiagonal operators arise in Rogers-Ramanujan identities. In this paper, we study the numerical ranges of these tridiagonal operators and finite-dimensional tridiagonal matrices. In particular, when r=−1, the numerical range of the finite-dimensional tridiagonal matrix is the convex hull of two explicit ellipses. Applying the result, we obtain that the numerical range of the tridiagonal operator is the square
10.
Mohamed Barraa Mohamed Boumazgour 《Journal of Mathematical Analysis and Applications》2003,286(1):359-362
Let be the algebra of bounded linear operators on a Hilbert space H. For , define the elementary operator MA,B by MA,B(X)=AXB (). We give necessary and sufficient conditions for any pair of operators A and B to satisfy the equation ‖I+MA,B‖=1+‖A‖‖B‖, where I is the identity operator on H. 相似文献
11.
Rosihan M. Ali V. Ravichandran 《Journal of Mathematical Analysis and Applications》2006,324(1):663-668
Let A,B,D,E∈[−1,1]. Conditions on A,B,D and E are determined so that
12.
Janusz Matkowski 《Journal of Mathematical Analysis and Applications》2008,348(1):315-323
Let (Ω,Σ,μ) a measure space such that 0<μ(A)<1<μ(B)<∞ for some A,B∈Σ. Under some natural conditions on the bijective functions φ,φ1,φ2,ψ,ψ1,ψ2:(0,∞)→(0,∞) we prove that if
13.
Nick Dungey 《Journal of Functional Analysis》2009,256(5):1387-1407
There is a standard notion of type for a sectorial linear operator acting in a Banach space. We introduce a notion of asymptotic type for a linear operator V, involving estimates on the resolvent −1(λI+V) as λ→0. We show, for example, that if V is sectorial and of asymptotic type ω then the fractional power Vα is of asymptotic type αω for a suitable range of positive α. Moreover, we establish various properties of the operator ; in particular, this operator is of asymptotic type 0, for a sectorial operator V. This result has an application to the construction of operators satisfying the well-known Ritt resolvent condition. 相似文献
14.
15.
Let K denote a field and let V denote a vector space over K with finite positive dimension.We consider a pair of K-linear transformations A:V→V and A∗:V→V that satisfy the following conditions: (i) each of A,A∗ is diagonalizable; (ii) there exists an ordering of the eigenspaces of A such that A∗Vi⊆Vi-1+Vi+Vi+1 for 0?i?d, where V-1=0 and Vd+1=0; (iii) there exists an ordering of the eigenspaces of A∗ such that for 0?i?δ, where and ; (iv) there is no subspace W of V such that AW⊆W,A∗W⊆W,W≠0,W≠V.We call such a pair a tridiagonal pair on V. It is known that d=δ and for 0?i?d the dimensions of coincide.In this paper we show that the following (i)-(iv) hold provided that K is algebraically closed: (i) Each of has dimension 1.(ii) There exists a nondegenerate symmetric bilinear form 〈,〉 on V such that 〈Au,v〉=〈u,Av〉 and 〈A∗u,v〉=〈u,A∗v〉 for all u,v∈V.(iii) There exists a unique anti-automorphism of End(V) that fixes each of A,A∗.(iv) The pair A,A∗ is determined up to isomorphism by the data , where θi (resp.) is the eigenvalue of A (resp.A∗) on Vi (resp.), and is the split sequence of A,A∗ corresponding to and . 相似文献
16.
Zinaida A. Lykova 《Journal of Pure and Applied Algebra》2006,205(3):471-497
We present methods for the computation of the Hochschild and cyclic-type continuous homology and cohomology of some locally convex strict inductive limits of Fréchet algebras Am. In the pure algebraic case it is known that, for the cyclic homology of A, for all n?0 [Cyclic Homology, Springer, Berlin, 1992, E.2.1.1]. We show that, for a locally convex strict inductive system of Fréchet algebras such that
0→Am→Am+1→Am+1/Am→0 相似文献
17.
Sefi Ladkani 《Linear algebra and its applications》2008,428(4):742-753
We show that for piecewise hereditary algebras, the periodicity of the Coxeter transformation implies the non-negativity of the Euler form. Contrary to previous assumptions, the condition of piecewise heredity cannot be omitted, even for triangular algebras, as demonstrated by incidence algebras of posets.We also give a simple, direct proof, that certain products of reflections, defined for any square matrix A with 2 on its main diagonal, and in particular the Coxeter transformation corresponding to a generalized Cartan matrix, can be expressed as , where A+, A- are closely associated with the upper and lower triangular parts of A. 相似文献
18.
Ali-Amir Husain 《Journal of Functional Analysis》2006,231(1):157-176
By analogy with the join in topology, the join A*B for operator algebras A and B acting on Hilbert spaces H and K, respectively, was defined by Gilfeather and Smith (Amer. J. Math. 116 (1994) 541-561). Assuming that K is finite dimensional, they calculated the Hochschild cohomology groups for A*B with coefficients in L(K⊕H). We assume that A is a maximal abelian von Neumann algebra acting on H, A is a subalgebra of , and B is an ultraweakly closed subalgebra of Mn(A) containing A⊗1n. We show that B may be decomposed into a finite sum of free modules. In this context, we redefine the join of A and B, generalize the calculations of Gilfeather and Smith, and calculate , for all m?0. 相似文献
19.
Bo Hou 《Linear algebra and its applications》2011,435(8):1987-1996
Let F denote a field and let V denote a vector space over F with finite positive dimension. We consider an ordered pair of F-linear transformations A:V→V and A∗:V→V that satisfy the following conditions: (i) each of A,A∗ is diagonalizable on V; (ii) there exists an ordering of the eigenspaces of A such that A∗Vi⊆V0+V1+?+Vi+1 for 0?i?d, where V-1:=0 and Vd+1:=0; (iii) there exists an ordering of the eigenspaces of A∗ such that for 0?i?δ, where and . We call such a pair a Hessenberg pair on V. It is known that if the Hessenberg pair A,A∗ on V is irreducible then d=δ and for 0?i?d the dimensions of Vi and coincide. We say a Hessenberg pair A,A∗ on V is sharp whenever it is irreducible and .In this paper, we give the definitions of a Hessenberg system and a sharp Hessenberg system. We discuss the connection between a Hessenberg pair and a Hessenberg system. We also define a finite sequence of scalars called the parameter array for a sharp Hessenberg system, which consists of the eigenvalue sequence, the dual eigenvalue sequence and the split sequence. We calculate the split sequence of a sharp Hessenberg system. We show that a sharp Hessenberg pair is a tridiagonal pair if and only if there exists a nonzero nondegenerate bilinear form on V that satisfies 〈Au,v〉=〈u,Av〉 and 〈A∗u,v〉=〈u,A∗v〉 for all u,v∈V. 相似文献
20.
For finite subsets A1,…,An of a field, their sumset is given by . In this paper, we study various restricted sumsets of A1,…,An with restrictions of the following forms: