共查询到20条相似文献,搜索用时 15 毫秒
1.
All-derivable points of operator algebras 总被引:1,自引:0,他引:1
Jun Zhu 《Linear algebra and its applications》2007,427(1):1-5
Let A be an operator subalgebra in B(H), where H is a Hilbert space. We say that an element Z∈A is an all-derivable point of A for the norm-topology (strongly operator topology, etc.) if, every norm-topology (strongly operator topology, etc.) continuous derivable linear mapping φ at Z (i.e. φ(ST)=φ(S)T+Sφ(T) for any S,T∈A with ST=Z) is a derivation. In this paper, we show that every invertible operator in the nest algebra is an all-derivable point of the nest algebra for the strongly operator topology. We also prove that every nonzero element of the algebra of all 2×2 upper triangular matrixes is an all-derivable point of the algebra. 相似文献
2.
Jordan derivations of triangular algebras 总被引:3,自引:0,他引:3
In this note, it is shown that every Jordan derivation of triangular algebras is a derivation. 相似文献
3.
Jun Zhu 《Linear algebra and its applications》2008,429(4):804-818
Let TMn be the algebra of all n×n upper triangular matrices. We say that an element G∈TMn is an all-derivable point of TMn if every derivable linear mapping φ at G (i.e. φ(ST)=φ(S)T+Sφ(T) for any S,T∈TMn with ST=G) is a derivation. In this paper we show that G∈TMn is an all derivable point of TMn if and only if G≠0. 相似文献
4.
Jordan higher derivations on triangular algebras 总被引:1,自引:0,他引:1
Zhankui Xiao 《Linear algebra and its applications》2010,432(10):2615-1054
In this paper, we show that any Jordan higher derivation on a triangular algebra is a higher derivation. This extends the main result in [13] to the case of higher derivations. 相似文献
5.
In this paper, it is shown that every norm continuous linear local derivation from an arbitrary CSL algebra whose lattice is generated by finitely many independent nests into any ultraweakly closed subalgebra which contains the algebra is an inner derivation, and that every norm continuous linear local derivation from an arbitrary CSL algebra whose lattice is completely distributive into any ultraweakly closed subalgebra which contains the algebra is a derivation. 相似文献
6.
Suppose that A is an operator algebra on a Hilbert space H. An element V in A is called an all-derivable point of A for the strong operator topology if every strong operator topology continuous derivable mapping φ at V is a derivation. Let N be a complete nest on a complex and separable Hilbert space H. Suppose that M belongs to N with {0}≠M≠H and write for M or M⊥. Our main result is: for any with , if is invertible in , then Ω is an all-derivable point in for the strong operator topology. 相似文献
7.
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
8.
Generalized Jordan derivations on triangular matrix algebras 总被引:2,自引:0,他引:2
In this note, we prove that every generalized Jordan derivation from the algebra of all upper triangular matrices over a commutative ring with identity into its bimodule is the sum of a generalized derivation and an antiderivation. 相似文献
9.
We show that weakly closed Jordan ideals in nest algebras on Banach spaces are associative ideals. The decomposability of
finite-rank operators in Jordan ideals and the commutants of bimodules are also investigated.
Author’s address: J. Li and F. Lu, Department of Mathematics, Suzhou University, Suzhou 215006, People’s Republic of China
This research was supported by NNSFC (No. 10771154) and PNSFJ (NO. BK2007049). 相似文献
10.
Let T be a triangular algebra over a commutative ring R. In this paper, under some mild conditions on T, we prove that if δ:T→T is an R-linear map satisfying
δ([x,y])=[δ(x),y]+[x,δ(y)] 相似文献
11.
Let be an operator algebra on a Hilbert space. We say that an element is an all-derivable point of for the strong operator topology if every strong operator topology continuous derivable linear mapping φ at G (i.e. φ(ST)=φ(S)T+Sφ(T) for any with ST=G) is a derivation. Let be a continuous nest on a complex and separable Hilbert space H. We show in this paper that every orthogonal projection operator P(M) () is an all-derivable point of for the strong operator topology. 相似文献
12.
Non-linear numerical radius isometries on atomic nest algebras and diagonal algebras 总被引:1,自引:0,他引:1
A nonlinear map φ between operator algebras is said to be a numerical radius isometry if w(φ(T−S))=w(T−S) for all T, S in its domain algebra, where w(T) stands for the numerical radius of T. Let and be two atomic nests on complex Hilbert spaces H and K, respectively. Denote the nest algebra associated with and the diagonal algebra. We give a thorough classification of weakly continuous numerical radius isometries from onto and a thorough classification of numerical radius isometries from onto . 相似文献
13.
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
14.
You Qing Ji 《Linear algebra and its applications》2011,434(10):2149-2157
In this paper, we estimate the stable ranks of a Banach algebra in terms of the stable ranks of its quotient algebra and ideal under the assumption that the quotient map splits. As an application, several results about the Bass and the connected stable ranks of nest algebras are obtained. 相似文献
15.
Jian-Hua Zhang Shan Feng Hong-Xia Li Rui-Hua Wu 《Linear algebra and its applications》2006,418(1):225-233
Let N be a nest on a complex separable Hilbert space H, and τ(N) be the associated nest algebra. In this paper, we prove that every biderivation of τ(N) is an inner biderivation if and only if dim 0+ ≠ 1 or , and that every generalized biderivation of τ(N) is an inner generalized biderivation if dim 0+ ≠ 1 and . 相似文献
16.
Jiankui Li 《Linear algebra and its applications》2010,432(1):5-322
For a commutative subspace lattice L in a von Neumann algebra N and a bounded linear map f:N∩algL→B(H), we show that if Af(B)C=0 for all A,B,C∈N∩algL satisfying AB=BC=0, then f is a generalized derivation. For a unital C∗-algebra A, a unital Banach A-bimodule M, and a bounded linear map f:A→M, we prove that if f(A)B=0 for all A,B∈A with AB=0, then f is a left multiplier; as a consequence, every bounded local derivation from a C∗-algebra to a Banach A-bimodule is a derivation. We also show that every local derivation on a semisimple free semigroupoid algebra is a derivation and every local multiplier on a free semigroupoid algebra is a multiplier. 相似文献
17.
In this paper we prove that every nonlinear Lie derivation of triangular algebras is the sum of an additive derivation and a map into its center sending commutators to zero. 相似文献
18.
19.
In this paper we describe some classes of linear operatorsTL(H) (mainly Toeplitz, Wiener-Hopf and singular integral) on a Hilbert spacesH such that the spectrum (T, L(H)) is continuous at the pointsT from these classes. We also describe some subalgebras
of the algebras for which the spectrum (x,) becomes continuous at the pointsx when (x,) is restricted to the subalgebra
. In particular, we show that the spectrum (x,) is continuous in Banach algebras with polynomial identities. Examples of such algebras are given.This research was partially supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities. 相似文献
20.
We answer, by counterexample, several questions concerning algebras of operators on a Hilbert space. The answers add further weight to the thesis that, for many purposes, such algebras ought to be studied in the framework of operator spaces, as opposed to that of Banach spaces and Banach algebras. In particular, the ‘nonselfadjoint analogue’ of a w*-algebra resides naturally in the category of dual operator spaces, as opposed to dual Banach spaces. We also show that an automatic w*-continuity result in the preceding paper of the authors, is sharp. 相似文献