共查询到20条相似文献,搜索用时 125 毫秒
1.
On derivable mappings 总被引:1,自引:0,他引:1
Jiankui Li 《Journal of Mathematical Analysis and Applications》2011,374(1):311-322
A linear mapping δ from an algebra A into an A-bimodule M is called derivable at c∈A if δ(a)b+aδ(b)=δ(c) for all a,b∈A with ab=c. For a norm-closed unital subalgebra A of operators on a Banach space X, we show that if C∈A has a right inverse in B(X) and the linear span of the range of rank-one operators in A is dense in X then the only derivable mappings at C from A into B(X) are derivations; in particular the result holds for all completely distributive subspace lattice algebras, J-subspace lattice algebras, and norm-closed unital standard algebras of B(X). As an application, every Jordan derivation from such an algebra into B(X) is a derivation. For a large class of reflexive algebras A on a Banach space X, we show that inner derivations from A into B(X) can be characterized by boundedness and derivability at any fixed C∈A, provided C has a right inverse in B(X). We also show that if A is a canonical subalgebra of an AF C∗-algebra B and M is a unital Banach A-bimodule, then every bounded local derivation from A into M is a derivation; moreover, every bounded linear mapping from A into B that is derivable at the unit I is a derivation. 相似文献
2.
Hongyan Zeng 《Linear algebra and its applications》2011,434(2):463-474
Let A be a Banach algebra with unity I and M be a unital Banach A-bimodule. A family of continuous additive mappings D=(δi)i∈N from A into M is called a higher derivable mapping at X, if δn(AB)=∑i+j=nδi(A)δj(B) for any A,B∈A with AB=X. In this paper, we show that D is a Jordan higher derivation if D is a higher derivable mapping at an invertible element X. As an application, we also get that every invertible operator in a nontrivial nest algebra is a higher all-derivable point. 相似文献
3.
Let B(X) be the algebra of all bounded linear operators on a complex Banach space X. We give the concrete form of every unital surjective map φ on B(X) such that AB is a non-zero idempotent if and only if φ(A)φ(B) is for all A,B∈B(X) when the dimension of X is at least 3. 相似文献
4.
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
5.
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
6.
Jiren Zhou 《Linear algebra and its applications》2011,435(8):1972-1986
Suppose that A is an algebra and M is an A-bimodule. Let A be any element in A. A linear mapping δ from A into M is said to be derivable at A if δ(ST)=δ(S)T+Sδ(T) for any S,T in A with ST=A. Given an algebra A, such as a non-abelian von Neumann algebra or an irreducible CDCSL algebra on a Hilbert space H with dimH?2, we show that there exists a nontrivial idempotent P in A such that for any Q∈PAP which is invertible in PAP, every linear mapping derivable at Q from A into some unital A-bimodule (for example, A or B(H)) is derivation. 相似文献
7.
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
8.
Xiaofei Qi 《Linear algebra and its applications》2010,432(12):3183-1146
Let N be a nest on a complex Banach space X with N∈N complemented in X whenever N-=N, and let AlgN be the associated nest algebra. We say that an operator Z∈AlgN is an all-derivable point of AlgN if every linear map δ from AlgN into itself derivable at Z (i.e. δ(A)B+Aδ(B)=δ(Z) for any A,B∈A with AB=Z) is a derivation. In this paper, it is shown that if Z∈AlgN is an injective operator or an operator with dense range, or an idempotent operator with ran(Z)∈N, then Z is an all-derivable point of AlgN. Particularly, if N is a nest on a complex Hilbert space, then every idempotent operator with range in N, every injective operator as well as every operator with dense range in AlgN is an all-derivable point of the nest algebra AlgN. 相似文献
9.
Changguo Wei 《Journal of Functional Analysis》2010,258(2):650-664
Let A be a unital separable nuclear C∗-algebra and let B be a stable C∗-algebra. Using K-theory and KK-theory we establish universal coefficient theorems for the stable Ext-groups of unital extensions of A by B when A and B have certain properties, which generalize a result of L. Brown and M. Dadarlat for the strong Ext-groups. The class of extensions being studied are also enlarged. 相似文献
10.
Let A⊂C(X) and B⊂C(Y) be uniform algebras with Choquet boundaries δA and δB. A map T:A→B is called norm-linear if ‖λTf+μTg‖=‖λf+μg‖; norm-additive, if ‖Tf+Tg‖=‖f+g‖, and norm-additive in modulus, if ‖|Tf|+|Tg|‖=‖|f|+|g|‖ for each λ,μ∈C and all algebra elements f and g. We show that for any norm-linear surjection T:A→B there exists a homeomorphism ψ:δA→δB such that |(Tf)(y)|=|f(ψ(y))| for every f∈A and y∈δB. Sufficient conditions for norm-additive and norm-linear surjections, not assumed a priori to be linear, or continuous, to be unital isometric algebra isomorphisms are given. We prove that any unital norm-linear surjection T for which T(i)=i, or which preserves the peripheral spectra of C-peaking functions of A, is a unital isometric algebra isomorphism. In particular, we show that if a linear operator between two uniform algebras, which is surjective and norm-preserving, is unital, or preserves the peripheral spectra of C-peaking functions, then it is automatically multiplicative and, in fact, an algebra isomorphism. 相似文献
11.
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.
12.
Yong-Soo Jung 《Journal of Mathematical Analysis and Applications》2008,339(1):108-114
Let A be a unital normed algebra and let M be a unitary Banach left A-module. If f:A→M is an approximate module left derivation, then f:A→M is a module left derivation. Moreover, if M=A is a semiprime unital Banach algebra and f(tx) is continuous in t∈R for each fixed x in A, then every approximately linear left derivation f:A→A is a linear derivation which maps A into the intersection of its center Z(A) and its Jacobson radical rad(A). In particular, if A is semisimple, then f is identically zero. 相似文献
13.
Bojan Magajna 《Journal of Mathematical Analysis and Applications》2008,342(2):1481-1484
A unital C∗-algebra A is weakly central if and only if for every x∈A there exists a sequence of elementary unital completely positive maps αn on A such that the sequence (αn(x)) converges to a central element. 相似文献
14.
R. Exel 《Journal of Functional Analysis》2007,244(1):26-62
Given a C∗-algebra B, a closed *-subalgebra A⊆B, and a partial isometry S in B which interacts with A in the sense that S∗aS=H(a)S∗S and SaS∗=V(a)SS∗, where V and H are positive linear operators on A, we derive a few properties which V and H are forced to satisfy. Removing B and S from the picture we define an interaction as being a pair of maps (V,H) satisfying the derived properties. Starting with an abstract interaction (V,H) over a C∗-algebra A we construct a C∗-algebra B containing A and a partial isometry S whose interaction with A follows the above rules. We then discuss the possibility of constructing a covariance algebra from an interaction. This turns out to require a generalization of the notion of correspondences (also known as Pimsner bimodules) which we call a generalized correspondence. Such an object should be seen as an usual correspondence, except that the inner-products need not lie in the coefficient algebra. The covariance algebra is then defined using a natural generalization of Pimsner's construction of the celebrated Cuntz-Pimsner algebras. 相似文献
15.
We prove that each 2-local derivation from the algebra Mn(A ) (n > 2) into its bimodule Mn(M) is a derivation, where A is a unital Banach algebra and M is a unital A -bimodule such that each Jordan derivation from A into M is an inner derivation, and that each 2-local derivation on a C*-algebra with a faithful traceable representation is a derivation. We also characterize local and 2-local Lie derivations on some algebras such as von Neumann algebras, nest algebras, the Jiang–Su algebra, and UHF algebras. 相似文献
16.
Jian YuDingtao Peng Shuwen Xiang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6326-6332
Let X be a nonempty, convex and compact subset of normed linear space E (respectively, let X be a nonempty, bounded, closed and convex subset of Banach space E and A be a nonempty, convex and compact subset of X) and f:X×X→R be a given function, the uniqueness of equilibrium point for equilibrium problem which is to find x∗∈X (respectively, x∗∈A) such that f(x∗,y)≥0 for all y∈X (respectively, f(x∗,y)≥0 for all y∈A) is studied with varying f (respectively, with both varying f and varying A). The results show that most of equilibrium problems (in the sense of Baire category) have unique equilibrium point. 相似文献
17.
Let R be a commutative ring with identity, A and B be unital algebras over R and M be a unital (it A,it B)-bimodule. Let be the triangular algebra consisting of A, it Band M. Motivated by the work of Cheung [14] we mainly consider the question whether every higher derivation on a triangular algebra is an inner higher derivation. We also give some characterizations on (generalized-)Jordan (triple-)higher derivations of triangular algebras. 相似文献
18.
Let AlgN be a nest algebra associated with the nest N on a (real or complex) Banach space X. Assume that every N∈N is complemented whenever N-=N. Let δ:AlgN→AlgN be an additive map. It is shown that the following three conditions are equivalent: (1) δ is derivable at zero point, i.e., δ(AB)=δ(A)B+Aδ(B) whenever AB=0; (2) δ is Jordan derivable at zero point, i.e., δ(AB+BA)=δ(A)B+Aδ(B)+Bδ(A)+δ(B)A whenever AB+BA=0; (3) δ has the form δ(A)=τ(A)+cA for some additive derivation τ and some scalar c. It is also shown that δ is generalized derivable at zero point, i.e., δ(AB)=δ(A)B+Aδ(B)-Aδ(I)B whenever AB=0, if and only if δ is an additive generalized derivation. Finer characterizations of above maps are given for the case dimX=∞. 相似文献
19.
Let (K,d) be a non-empty, compact metric space and α∈]0,1[. Let A be either lipα(K) or Lipα(K) and let B be a commutative unital Banach algebra. We show that every continuous linear map T:A→B with the property that T(f)T(g)=0 whenever f,g∈A are such that fg=0 is of the form T=wΦ for some invertible element w in B and some continuous epimorphism Φ:A→B. 相似文献
20.
Generalized Lie derivations on triangular algebras 总被引:1,自引:0,他引:1
Dominik Benkovi? 《Linear algebra and its applications》2011,434(6):1532-1544
Let A be a unital algebra and let M be a unitary A-bimodule. We consider generalized Lie derivations mapping from A to M. Our results are applied to triangular algebras, in particular to nest algebras and (block) upper triangular matrix algebras. We prove that under certain conditions each generalized Lie derivation of a triangular algebra A is the sum of a generalized derivation and a central map which vanishes on all commutators of A. 相似文献