共查询到20条相似文献,搜索用时 140 毫秒
1.
B.P. Duggal 《Journal of Mathematical Analysis and Applications》2010,370(2):584-587
Let B(H) denote the algebra of operators on an infinite dimensional complex Hilbert space H, and let A○∈B(K) denote the Berberian extension of an operator A∈B(H). It is proved that the set theoretic function σ, the spectrum, is continuous on the set C(i)⊂B(Hi) of operators A for which σ(A)={0} implies A is nilpotent (possibly, the 0 operator) and at every non-zero λ∈σp(A○) for some operators X and B such that λ∉σp(B) and σ(A○)={λ}∪σ(B). If CS(m) denotes the set of upper triangular operator matrices , where Aii∈C(i) and Aii has SVEP for all 1?i?m, then σ is continuous on CS(m). It is observed that a considerably large number of the more commonly considered classes of Hilbert space operators constitute sets C(i) and have SVEP. 相似文献
2.
A.B. Aleksandrov 《Journal of Functional Analysis》2010,258(11):3675-5251
This is a continuation of our paper [2]. We prove that for functions f in the Hölder class Λα(R) and 1<p<∞, the operator f(A)−f(B) belongs to Sp/α, whenever A and B are self-adjoint operators with A−B∈Sp. We also obtain sharp estimates for the Schatten-von Neumann norms ‖f(A)−f(B)Sp/α‖ in terms of ‖A−BSp‖ and establish similar results for other operator ideals. We also estimate Schatten-von Neumann norms of higher order differences . We prove that analogous results hold for functions on the unit circle and unitary operators and for analytic functions in the unit disk and contractions. Then we find necessary conditions on f for f(A)−f(B) to belong to Sq under the assumption that A−B∈Sp. We also obtain Schatten-von Neumann estimates for quasicommutators f(A)R−Rf(B), and introduce a spectral shift function and find a trace formula for operators of the form f(A−K)−2f(A)+f(A+K). 相似文献
3.
Alain Escassut 《Topology and its Applications》2006,153(7):1152-1163
Let L be a field complete for a non-trivial ultrametric absolute value and let (A,‖⋅‖) be a commutative normed L-algebra with unity whose spectral semi-norm is ‖⋅‖si. Let Mult(A,‖⋅‖) be the set of continuous multiplicative semi-norms of A, let S be the Shilov boundary for (A,‖⋅‖si) and let ψ∈Mult(A,‖⋅‖si). Then ψ belongs to S if and only if for every neighborhood U of ψ in Mult(A,‖⋅‖), there exists θ∈U and g∈A satisfying ‖g‖si=θ(g) and . Suppose A is uniform, let f∈A and let Z(f)={?∈Mult(A,‖⋅‖)|?(f)=0}. Then f is a topological divisor of zero if and only if there exists ψ∈S such that ψ(f)=0. Suppose now A is complete. If f is not a divisor of zero, then it is a topological divisor of zero if and only if the ideal fA is not closed in A. Suppose A is ultrametric, complete and Noetherian. All topological divisors of zero are divisors of zero. This applies to affinoid algebras. Let A be a Krasner algebra H(D) without non-trivial idempotents: an element f∈H(D) is a topological divisor of zero if and only if fH(D) is not a closed ideal; moreover, H(D) is a principal ideal ring if and only if it has no topological divisors of zero but 0 (this new condition adds to the well-known set of equivalent conditions found in 1969). 相似文献
4.
Let N denote the set of positive integers. The asymptotic density of the set A⊆N is d(A)=limn→∞|A∩[1,n]|/n, if this limit exists. Let AD denote the set of all sets of positive integers that have asymptotic density, and let SN denote the set of all permutations of the positive integers N. The group L? consists of all permutations f∈SN such that A∈AD if and only if f(A)∈AD, and the group L* consists of all permutations f∈L? such that d(f(A))=d(A) for all A∈AD. Let be a one-to-one function such that d(f(N))=1 and, if A∈AD, then f(A)∈AD. It is proved that f must also preserve density, that is, d(f(A))=d(A) for all A∈AD. Thus, the groups L? and L* coincide. 相似文献
5.
Let [n] denote the set of positive integers {1,2,…,n}. An r-partial permutation of [n] is a pair (A,f) where A⊆[n], |A|=r and f:A→[n] is an injective map. A set A of r-partial permutations is intersecting if for any (A,f), (B,g)∈A, there exists x∈A∩B such that f(x)=g(x). We prove that for any intersecting family A of r-partial permutations, we have .It seems rather hard to characterize the case of equality. For 8?r?n-3, we show that equality holds if and only if there exist x0 and ε0 such that A consists of all (A,f) for which x0∈A and f(x0)=ε0. 相似文献
6.
For A∈B(X), B∈B(Y) and C∈B(Y,X), let MC be the operator defined on X⊕Y by . In this paper, we study defect set (Σ(A)∪Σ(B))?Σ(MC), where Σ is the Browder spectrum, the essential approximate point spectrum and Browder essential approximate point spectrum. We then give application for Weyl's and Browder's theorems. 相似文献
7.
Refael Hassin 《Operations Research Letters》2005,33(3):242-248
The input to the MAXIMUM SAVING PARTITION PROBLEM consists of a set V={1,…,n}, weights wi, a function f, and a family S of feasible subsets of V. The output is a partition (S1,…,Sl) such that Si∈S, and is maximized. We present a general -approximation algorithm, and improved algorithms for special cases of the function f. 相似文献
8.
Piotr Niemiec 《Topology and its Applications》2008,155(12):1323-1328
The aim of the paper is to generalize the notion of the Haar integral. For a compact semigroup S acting continuously on a Hausdorff compact space Ω, the algebra A(S)⊂C(Ω,R) of S-invariant functions and the linear space M(S) of S-invariant (real-valued) finite signed measures are considered. It is shown that if S has a left and right invariant measure, then the dual space of A(S) is isometrically lattice-isomorphic to M(S) and that there exists a unique linear operator (called the Haar integral) such that for each f∈A(S) and for any f∈C(Ω,R) and s∈S, , where . 相似文献
9.
Lajos Molnár 《Journal of Mathematical Analysis and Applications》2007,327(1):302-309
Let H be a Hilbert space and let A and B be standard ∗-operator algebras on H. Denote by As and Bs the set of all self-adjoint operators in A and B, respectively. Assume that and are surjective maps such that M(AM∗(B)A)=M(A)BM(A) and M∗(BM(A)B)=M∗(B)AM∗(B) for every pair A∈As, B∈Bs. Then there exist an invertible bounded linear or conjugate-linear operator and a constant c∈{−1,1} such that M(A)=cTAT∗, A∈As, and M∗(B)=cT∗BT, B∈Bs. 相似文献
10.
Let B(X) be the algebra of all bounded linear operators on the Banach space X, and let N(X) be the set of nilpotent operators in B(X). Suppose ?:B(X)→B(X) is a surjective map such that A,B∈B(X) satisfy AB∈N(X) if and only if ?(A)?(B)∈N(X). If X is infinite dimensional, then there exists a map f:B(X)→C?{0} such that one of the following holds:
- (a)
- There is a bijective bounded linear or conjugate-linear operator S:X→X such that ? has the form A?S[f(A)A]S-1.
- (b)
- The space X is reflexive, and there exists a bijective bounded linear or conjugate-linear operator S : X′ → X such that ? has the form A ? S[f(A)A′]S−1.
11.
Sergiu Aizicovici Veli-Matti Hokkanen 《Journal of Mathematical Analysis and Applications》2004,292(2):540-557
The solvability of the evolution system v′(t)+B(t)u(t)∋f(t), v(t)∈A(t)u(t), 0<t<T, with the periodic condition v(0)=v(T) is investigated in the case where are bounded, possibly degenerate, subdifferentials and are unbounded subdifferentials. 相似文献
12.
Chi-Kwong Li 《Linear algebra and its applications》2009,431(12):2336-2345
Let B(H) be the algebra of bounded linear operator acting on a Hilbert space H (over the complex or real field). Characterization is given to A1,…,Ak∈B(H) such that for any unitary operators is always in a special class S of operators such as normal operators, self-adjoint operators, unitary operators. As corollaries, characterizations are given to A∈B(H) such that complex, real or nonnegative linear combinations of operators in its unitary orbit U(A)={U∗AU:Uunitary} always lie in S. 相似文献
13.
Charles C.C. Li 《Journal of Number Theory》2004,104(1):177-192
Let (X,μ) be a measurable topological space. Let S1,S2,… be a family of finite subsets of X. Suppose each x∈Si has a weight wix∈R+ assigned to it. We say {Si} is {wi}-distributed with respect to the measure μ if for any continuous function f on X, we have .Let S(N,k) be the space of modular cusp forms over Γ0(N) of weight k and let be a basis which consists of Hecke eigenforms. Let ar(h) be the rth Fourier coefficient of h. Let xph be the eigenvalue of h relative to the normalized Hecke operator T′p. Let ||·|| be the Petersson norm on S(N,k). In this paper we will show that for any even integer k?3, is -distributed with respect to a polynomial times the Sato-Tate measure when N→∞. 相似文献
14.
When A∈B(H) and B∈B(K) are given, we denote by MC the operator matrix acting on the infinite-dimensional separable Hilbert space H⊕K of the form In this paper, for given A and B, the sets and ?C∈Inv(K,H)σl(MC) are determined, where σl(T),Bl(K,H) and Inv(K,H) denote, respectively, the left spectrum of an operator T, the set of all the left invertible operators and the set of all the invertible operators from K into H. 相似文献
15.
Dhruv Mubayi 《Journal of Combinatorial Theory, Series A》2006,113(3):547-550
Fix integers k?3 and n?3k/2. Let F be a family of k-sets of an n-element set so that whenever A,B,C∈F satisfy |A∪B∪C|?2k, we have A∩B∩C≠∅. We prove that with equality only when ?F∈FF≠∅. This settles a conjecture of Frankl and Füredi [2], who proved the result for n?k2+3k. 相似文献
16.
17.
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
18.
Rostislav Caha 《Discrete Mathematics》2007,307(16):2053-2066
A set A of vertices of a hypercube is called balanced if . We prove that for every natural number n there exists a natural number π1(n) such that for every hypercube Q with dim(Q)?π1(n) there exists a family of pairwise vertex-disjoint paths Pi between Ai and Bi for i=1,2,…,n with if and only if {Ai,Bi∣i=1,2,…,n} is a balanced set. 相似文献
19.
Chris J. Conidis 《Annals of Pure and Applied Logic》2010,162(1):83-88
We prove that if S is an ω-model of weak weak König’s lemma and , is incomputable, then there exists , such that A and B are Turing incomparable. This extends a recent result of Ku?era and Slaman who proved that if S0 is a Scott set (i.e. an ω-model of weak König’s lemma) and A∈S0, A⊆ω, is incomputable, then there exists B∈S0, B⊆ω, such that A and B are Turing incomparable. 相似文献
20.
In 1967 Komlós proved that for any sequence n{fn} in L1(μ), with ‖fn‖?M<∞ (where μ is a probability measure), there exists a subsequence n{gn} of n{fn} and a function g∈L1(μ) such that for any further subsequence n{hn} of n{gn},