共查询到20条相似文献,搜索用时 46 毫秒
1.
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
2.
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
3.
Quoc-Phong Vu 《Journal of Mathematical Analysis and Applications》2007,334(1):487-501
We study properties of solutions of the evolution equation , where B is a closable operator on the space AP(R,H) of almost periodic functions with values in a Hilbert space H such that B commutes with translations. The operator B generates a family of closed operators on H such that (whenever eiλtx∈D(B)). For a closed subset Λ⊂R, we prove that the following properties (i) and (ii) are equivalent: (i) for every function f∈AP(R,H) such that σ(f)⊆Λ, there exists a unique mild solution u∈AP(R,H) of Eq. (∗) such that σ(u)⊆Λ; (ii) is invertible for all λ∈Λ and . 相似文献
4.
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
5.
Danilo Royer 《Journal of Mathematical Analysis and Applications》2006,323(1):33-41
Given a local homeomorphism where U⊆X is clopen and X is a compact and Hausdorff topological space, we obtain the possible transfer operators Lρ which may occur for given by α(f)=f○σ. We obtain examples of partial dynamical systems (XA,σA) such that the construction of the covariance algebra C∗(XA,σA), proposed by B.K. Kwasniewski, and the crossed product by a partial endomorphism O(XA,α,L), recently introduced by the author and R. Exel, associated to this system are not equivalent, in the sense that there does not exist an invertible function ρ∈C(U) such that O(XA,α,Lρ)≅C∗(XA,σA). 相似文献
6.
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 a 2×2 operator matrix MC is upper semi-Fredholm and ind(MC)?0 for some C∈B(K,H) if and only if A is upper semi-Fredholm and
7.
B.P. Duggal 《Journal of Mathematical Analysis and Applications》2005,312(2):502-513
A Hilbert space operator T∈B(H) is hereditarily normaloid (notation: T∈HN) if every part of T is normaloid. An operator T∈HN is totally hereditarily normaloid (notation: T∈THN) if every invertible part of T is normaloid. We prove that THN-operators with Bishop's property (β), also THN-contractions with a compact defect operator such that and non-zero isolated eigenvalues of T are normal, are not supercyclic. Take A and B in THN and let dAB denote either of the elementary operators in B(B(H)): ΔAB and δAB, where ΔAB(X)=AXB−X and δAB(X)=AX−XB. We prove that if non-zero isolated eigenvalues of A and B are normal and , then dAB is an isoloid operator such that the quasi-nilpotent part H0(dAB−λ) of dAB−λ equals −1(dAB−λ)(0) for every complex number λ which is isolated in σ(dAB). If, additionally, dAB has the single-valued extension property at all points not in the Weyl spectrum of dAB, then dAB, and the conjugate operator , satisfy Weyl's theorem. 相似文献
8.
Joseph A. Ball Vladimir Bolotnikov 《Journal of Mathematical Analysis and Applications》2008,341(1):519-539
An interesting and recently much studied generalization of the classical Schur class is the class of contractive operator-valued multipliers S(λ) for the reproducing kernel Hilbert space H(kd) on the unit ball Bd⊂Cd, where kd is the positive kernel kd(λ,ζ)=1/(1−〈λ,ζ〉) on Bd. The reproducing kernel space H(KS) associated with the positive kernel KS(λ,ζ)=(I−S(λ)S∗(ζ))⋅kd(λ,ζ) is a natural multivariable generalization of the classical de Branges-Rovnyak canonical model space. A special feature appearing in the multivariable case is that the space H(KS) in general may not be invariant under the adjoints of the multiplication operators on H(kd). We show that invariance of H(KS) under for each j=1,…,d is equivalent to the existence of a realization for S(λ) of the form S(λ)=D+C−1(I−λ1A1−?−λdAd)(λ1B1+?+λdBd) such that connecting operator has adjoint U∗ which is isometric on a certain natural subspace (U is “weakly coisometric”) and has the additional property that the state operators A1,…,Ad pairwise commute; in this case one can take the state space to be the functional-model space H(KS) and the state operators A1,…,Ad to be given by (a de Branges-Rovnyak functional-model realization). We show that this special situation always occurs for the case of inner functions S (where the associated multiplication operator MS is a partial isometry), and that inner multipliers are characterized by the existence of such a realization such that the state operators A1,…,Ad satisfy an additional stability property. 相似文献
9.
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
10.
B.P. Duggal 《Linear algebra and its applications》2008,428(4):1109-1116
A Hilbert space operator A∈B(H) is p-hyponormal, A∈(p-H), if |A∗|2p?|A|2p; an invertible operator A∈B(H) is log-hyponormal, A∈(?-H), if log(TT∗)?log(T∗T). Let dAB=δAB or ?AB, where δAB∈B(B(H)) is the generalised derivation δAB(X)=AX-XB and ?AB∈B(B(H)) is the elementary operator ?AB(X)=AXB-X. It is proved that if A,B∗∈(?-H)∪(p-H), then, for all complex λ, , the ascent of (dAB-λ)?1, and dAB satisfies the range-kernel orthogonality inequality ‖X‖?‖X-(dAB-λ)Y‖ for all X∈(dAB-λ)-1(0) and Y∈B(H). Furthermore, isolated points of σ(dAB) are simple poles of the resolvent of dAB. A version of the elementary operator E(X)=A1XA2-B1XB2 and perturbations of dAB by quasi-nilpotent operators are considered, and Weyl’s theorem is proved for dAB. 相似文献
11.
N. Castro-González J.Y. Vélez-Cerrada 《Journal of Mathematical Analysis and Applications》2008,341(2):1213-1223
Given a bounded operator A on a Banach space X with Drazin inverse AD and index r, we study the class of group invertible bounded operators B such that I+AD(B−A) is invertible and R(B)∩N(Ar)={0}. We show that they can be written with respect to the decomposition X=R(Ar)⊕N(Ar) as a matrix operator, , where B1 and are invertible. Several characterizations of the perturbed operators are established, extending matrix results. We analyze the perturbation of the Drazin inverse and we provide explicit upper bounds of ‖B?−AD‖ and ‖BB?−ADA‖. We obtain a result on the continuity of the group inverse for operators on Banach spaces. 相似文献
12.
Wen Zhang 《Linear algebra and its applications》2011,435(6):1326-1335
Let A and B be (not necessarily unital or closed) standard operator algebras on complex Banach spaces X and Y, respectively. For a bounded linear operator A on X, the peripheral spectrum σπ(A) of A is the set σπ(A)={z∈σ(A):|z|=maxω∈σ(A)|ω|}, where σ(A) denotes the spectrum of A. Assume that Φ:A→B is a map the range of which contains all operators of rank at most two. It is shown that the map Φ satisfies the condition that σπ(BAB)=σπ(Φ(B)Φ(A)Φ(B)) for all A,B∈A if and only if there exists a scalar λ∈C with λ3=1 and either there exists an invertible operator T∈B(X,Y) such that Φ(A)=λTAT-1 for every A∈A; or there exists an invertible operator T∈B(X∗,Y) such that Φ(A)=λTA∗T-1 for every A∈A. If X=H and Y=K are complex Hilbert spaces, the maps preserving the peripheral spectrum of the Jordan skew semi-triple product BA∗B are also characterized. Such maps are of the form A?UAU∗ or A?UAtU∗, where U∈B(H,K) is a unitary operator, At denotes the transpose of A in an arbitrary but fixed orthonormal basis of H. 相似文献
13.
Browder spectra for upper triangular operator matrices 总被引:1,自引:0,他引:1
Xiaohong Cao 《Journal of Mathematical Analysis and Applications》2008,342(1):477-484
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, we prove that
14.
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
15.
When A∈B(H) and B∈B(K) are given, we denote by MC the operator acting on the Hilbert space H⊕K of the form . In this note, it is shown that the following results in [Hai-Yan Zhang, Hong-Ke Du, Browder spectra of upper-triangular operator matrices, J. Math. Anal. Appl. 323 (2006) 700-707]
16.
Chun-Gil Park 《Journal of Mathematical Analysis and Applications》2005,307(2):753-762
It is shown that every almost linear bijection of a unital C∗-algebra A onto a unital C∗-algebra B is a C∗-algebra isomorphism when h(n2uy)=h(n2u)h(y) for all unitaries u∈A, all y∈A, and n=0,1,2,…, and that almost linear continuous bijection of a unital C∗-algebra A of real rank zero onto a unital C∗-algebra B is a C∗-algebra isomorphism when h(n2uy)=h(n2u)h(y) for all , all y∈A, and n=0,1,2,…. Assume that X and Y are left normed modules over a unital C∗-algebra A. It is shown that every surjective isometry , satisfying T(0)=0 and T(ux)=uT(x) for all x∈X and all unitaries u∈A, is an A-linear isomorphism. This is applied to investigate C∗-algebra isomorphisms between unital C∗-algebras. 相似文献
17.
El Hassan Zerouali Hassane Zguitti 《Journal of Mathematical Analysis and Applications》2006,324(2):992-1005
For A∈L(X), B∈L(Y) and C∈L(Y,X) we denote by MC the operator defined on X⊕Y by . In this article, we study defect set DΣ=(Σ(A)∪Σ(B))?Σ(MC) for different spectra including the spectrum, the essential spectrum, Weyl spectrum and the approximate point spectrum. We then apply the obtained results to the stability of such spectra (DΣ=∅) and the classes of operators C for which stability holds of MC using local spectral theory. 相似文献
18.
Tahl Nowik 《Topology and its Applications》2007,154(9):1881-1893
Let F be a closed non-orientable surface. We classify all finite order invariants of immersions of F into R3, with values in any Abelian group. We show they are all functions of a universal order 1 invariant which we construct as T⊕P⊕Q, where T is a Z valued invariant reflecting the number of triple points of the immersion, and P,Q are Z/2 valued invariants characterized by the property that for any regularly homotopic immersions , P(i)−P(j)∈Z/2 (respectively, Q(i)−Q(j)∈Z/2) is the number mod 2 of tangency points (respectively, quadruple points) occurring in any generic regular homotopy between i and j.For immersion and diffeomorphism such that i and i○h are regularly homotopic we show:
P(i○h)−P(i)=Q(i○h)−Q(i)=(rank(h∗−Id)+ε(deth∗∗))mod2 相似文献
19.
Stevo Stevi? 《Applied mathematics and computation》2010,215(11):3817-5421
Let H(B) denote the space of all holomorphic functions on the open unit ball B of Cn and g∈H(B). We characterize the boundedness and compactness of the following integral-type operator
20.
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