共查询到20条相似文献,搜索用时 15 毫秒
1.
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
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.
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
4.
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
5.
Mohammad Gholampour 《Quaestiones Mathematicae》2018,41(2):227-238
We prove that every generalized Jordan derivation D from a JB?-algebra 𝒜 into itself or into its dual space is automatically continuous. In particular, we establish that every generalized Jordan derivation from a C?-algebra to a Jordan Banach module is continuous. As a consequence, every generalized derivation from a C?-algebra to a Banach bimodule is continuous. 相似文献
6.
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
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.
Wu Jing 《Quaestiones Mathematicae》2016,39(8):1037-1046
Let ? be an infinite dimensional complex Hilbert space and 𝒜 be a standard operator algebra on ? which is closed under the adjoint operation. We prove that every nonlinear *-Lie derivation δ of 𝒜 is automatically linear. Moreover, δ is an inner *-derivation. 相似文献
9.
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
10.
Mourre’s commutator theory is a powerful tool to study the continuous spectrum of self-adjoint operators and to develop scattering
theory. We propose a new approach of its main result, namely the derivation of the limiting absorption principle (LAP) from
a so called Mourre estimate. We provide a new interpretation of this result.
Received: September 20, 2006. Revised: February 1, 2007. 相似文献
11.
12.
《Quaestiones Mathematicae》2013,36(7):857-884
AbstractLet be a standard operator algebra on an infinite dimensional complex Hilbert space containing identity operator I. In this paper it is shown that if is closed under the adjoint operation, then every multiplicative ?-Lie triple derivation is a linear ?-derivation. Moreover, if there exists an operator S ∈ such that S + S? = 0 then d(U) = U S ? SU for all U ∈ , that is, d is inner. Furthermore, it is also shown that any multiplicative ?-Lie triple higher derivation D = {δn}n∈? of is automatically a linear inner higher derivation on with d(U)? = d(U?). 相似文献
13.
John Boris Miller 《Aequationes Mathematicae》1982,25(1):42-51
An operator form of the Euler-Maclaurin sum formula is obtained, expressing the sum of the Euler-Maclaurin infinite series in an inner derivation as the difference between a summation operator and an inner antiderivation, on a closed subalgebra of a Banach algebra. 相似文献
14.
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
15.
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
16.
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
17.
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
18.
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
19.
If E is a separable symmetric sequence space with trivial Boyd indices and
is the corresponding ideal of compact operators, then there exists a C1-function fE, a self-adjoint element
and a densely defined closed symmetric derivation δ on
such that
, but
相似文献
20.
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