排序方式: 共有43条查询结果,搜索用时 93 毫秒
1.
We present a new simple proof of the structural result for elementary operators on standard operator algebras. Using the idea of this short proof we can characterize surjective maps between standard operator algebras having a certain multiplicativity-like property appearing in the abstract definition of elementary operators of length one. In particular, we show that such maps are automatically additive. 相似文献
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We characterize linear rank-k nonincreasing, rank-k preserving, and corank-k preserving maps on B(H), the algebra of all bounded linear operators on the Hilbert space H. This unifies and extends finite-dimensional results and results on linear rank-1 non-increasing and rank-1 preserving maps in the infinite-dimensional case. We conclude with an application to *-semigroup isomorphisms of operator ideals. 相似文献
4.
Peter Šemrl 《Journal of Mathematical Analysis and Applications》2010,371(2):403-406
Let X be an infinite-dimensional separable real or complex Banach space and A a closed standard operator algebra on X. Then every local automorphism of A is an automorphism. The assumptions of infinite-dimensionality, separability, and closeness are all indispensable. 相似文献
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Peter Šemrl 《Aequationes Mathematicae》1986,31(1):184-190
LetX be a leftA-module, whereA is either a complex Banach *-algebra with an identity element or the field of quaternions. The main result of this note is that forQ, anA-quadratic functional defined onX, there exists a sesquilinear functionalB such thatB(x,x)=Q(x) holds for allxX. 相似文献
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It is proved that a linear transformation on the vector space of upper triangular matrices that maps the set of matrices of minimal rank 1 into itself, and either has the analogous property with respect to matrices of full minimal rank, or is bijective, is a triangular equivalence, or a flip about the south-west north-east diagonal followed by a triangular equivalence. The result can be regarded as an analogue of Marcus–Moyls theorem in the context of triangular matrices. 相似文献
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We describe the general form of bijective orthogonality preserving maps on ? n equipped with a pair of generalized indefinite inner products. The relations between the projective space and vector space versions of this result are examined and an example is given showing that the hypotheses of our main theorem are essential. 相似文献
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P. Šemrl 《Aequationes Mathematicae》1999,58(1-2):157-162
9.
Some linear preserver problems on upper triangular matrices 总被引:4,自引:0,他引:4
We consider linear preserver problems on the algebra of upper triangular matrices. We obtain the general form of nonsingular linear maps preserving rank one idempotents or commutativity. We give examples to show that the nonsingularity assumption is essential in our results. 相似文献
10.
We describe the general form of bijective maps on the space of all Hilbert space effects or all observables on a finite dimensional
space which preserve the spectral order in both directions.
The first author was supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. T043080, T046203,
and the second author was partially supported by a grant from the Ministry of Science of Slovenia. Both authors were supported
by a joint Hungarian-Slovene grant, Reg. No. SLO-5/05. 相似文献