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A nonlinear map φ between operator algebras is said to be a numerical radius isometry if w(φ(TS))=w(TS) 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
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Completely rank nonincreasing linear maps on nest algebras   总被引:1,自引:0,他引:1  
In this paper, the completely rank nonincreasing bounded linear maps on nest algebras acting on separable Hilbert spaces are characterized, and an affirmative answer to a problem posed by Hadwin and Larson is given for the case of such nest algebras.

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4.
Maps completely preserving spectral functions   总被引:1,自引:0,他引:1  
Let X,Y be infinite dimensional complex Banach spaces and A,B be standard operator algebras on X and Y, respectively. In this paper, we show that surjective maps completely preserving certain spectral function Δ(·) from A to B are isomorphisms, where Δ(·) stands for any one of 13 spectral functions σ(·), σl(·), σr(·), σl(·)∩σr(·), σ(·), ησ(·), σp(·), σc(·), σp(·)∩σc(·), σp(·)∪σc(·), σap(·), σs(·), and σap(·)∩σs(·).  相似文献
5.
Let X, Y be real or complex Banach spaces with dimension greater than 2 and let A, B be standard operator algebras on X and Y, respectively. In this paper, we show that every map completely preserving idempotence from A onto B is either an isomorphism or (in the complex case) a conjugate isomorphism; every map completely preserving square-zero from A onto B is a scalar multiple of either an isomorphism or (in the complex case) a conjugate isomorphism.  相似文献
6.
Additive maps derivable or Jordan derivable at zero point on nest algebras   总被引:1,自引:0,他引:1  
Let AlgN be a nest algebra associated with the nest N on a (real or complex) Banach space X. Assume that every NN 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
7.
Additive maps preserving Jordan zero-products on nest algebras   总被引:1,自引:0,他引:1  
Let and be nest algebras associated with the nests and on Banach Spaces. Assume that and are complemented whenever N-=N and M-=M. Let be a unital additive surjection. It is shown that Φ preserves Jordan zero-products in both directions, that is Φ(A)Φ(B)+Φ(B)Φ(A)=0AB+BA=0, if and only if Φ is either a ring isomorphism or a ring anti-isomorphism. Particularly, all unital additive surjective maps between Hilbert space nest algebras which preserves Jordan zero-products are characterized completely.  相似文献
8.
Let be a complex Hilbert space, the algebra of all bounded linear operators on and the real linear space of all self-adjoint operators on . We characterize the surjective maps on or that preserve the numerical ranges of products or Jordan triple-products of operators.

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9.
Let be a complex Hilbert space, be the algebra of all bounded linear operators on , be the subset of all selfadjoint operators in and or . Denote by the numerical radius of . We characterize surjective maps that satisfy for all without the linearity assumption.

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10.
We show that every unital linear bijection which preserves the maximal left ideals from a semi-simple Banach algebra onto a C-algebra of real rank zero is a Jordan isomorphism. Furthermore, every unital self-adjoint linear bijection on a countably decomposable factor von Neumann algebra is maximal left ideal preserving if and only if it is a *-automorphism.

  相似文献

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