Results 1 to 10 of about 122 (106)
Characterizing operations preserving separability measures via linear preserver problems [PDF]
Linear and Multilinear Algebra, 2011 We use classical results from the theory of linear preserver problems to characterize operators that send the set of pure states with Schmidt rank no greater than k back into itself, extending known results characterizing operators that send separable pure states to separable pure states.
Nathaniel Johnston
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Applying functional identities to some linear preserver problems [PDF]
Pacific Journal of Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
K I Beidar, M A Chebotar, M Brešar
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Some general techniques on linear preserver problems
Linear Algebra and Its Applications, 2000 Linear preserver problems are those of the following kind: characterize the linear mappings of one vector space of matrices into another that preserve given matrix properties (such as the rank or being symmetric). After listing various general techniques that have been devised for attacking such problems, the authors put forward three more of their own.
Peter Šemrl +2 more
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A localization technique for linear preserver problems
Linear Algebra and Its Applications, 2010 Let \(m,n\) be positive integers and \(\mathbb{F}\) a commutative field. A linear map \(\phi : M_{m,n}(\mathbb{F}) \rightarrow M_{m,n}(\mathbb{F})\) which preserves certain ``something'' (a property, a subset, etc.) is called a linear preserver. A common question is to ask whether a linear preserver is of standard form, i.e., there exist invertible ...
Peter Šemrl, Leiba Rodman
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Linear preserver problems and algebraic groups
Mathematische Annalen, 1995 Let \(M_n=M_n(K)\) be the space of \(n\) by \(n\) matrices over an algebraically closed field \(K\) of characteristic 0. We have a direct decomposition \(M_n=M^0_n\oplus K\cdot 1\), where 1 denotes the identity matrix, and \(M^0_n\) the subspace defined by \(\text{tr}(x)=0\).
Platonov, V.P., Dokovic, D.Z.
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Finite Reflection Groups and Linear Preserver Problems
Rocky Mountain Journal of Mathematics, 2004 Let \(G\) be a Coxeter group and \(V\) a Euclidean space such that \(G\subset \text{End}\,V\). Let \({\mathcal L}(G)\) be the set of linear transformations \(\Phi\) in \(\text{ End}\,V\) such that \(\Phi(G)=G\). Let \(P,Q\) be in the normalizer \(N(G)\) of \(G\) in the orthogonal group \(O(V)\) and assume that \(PQ\in G\).
Chi-Kwong Li
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Overgroups of some classical linear groups with applications to linear preserver problems
Linear Algebra and Its Applications, 1994 The authors give a description of all possible subgroups which contain a given subgroup \(G_ 0\) of some linear group \(G\). As an application of the results various linear preserver problems are solved.
Chi-Kwong Li, Dragomir Z ĐOKOVIĆ
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Linear preserver problems: A brief introduction and some special techniques
Linear Algebra and Its Applications, 1992 Let \(M\) be any one of the following matrix spaces: the set of all \(m\times n\) matrices over the field \(\mathbb{F}\), where usually \(\mathbb{F}\) is \(\mathbb{R}\) or \(\mathbb{C}\); the set of all \(n\times n\) symmetric matrices over \(\mathbb{F}\); the set of all \(n\times n\) skew-symmetric matrices over \(\mathbb{F}\); the set of all ...
Chi-Kwong Li, Nam-Kiu Tsing
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The Linear Coordinate Preserving Problem [PDF]
Communications in Algebra, 2008 We prove that every K-endomorphism of a rank 2 polynomial algebra over an algebraically closed field K of positive characteristic taking all linear coordinates to coordinates is an automorphism. We give a new characterization of coordinates of K[t][x, y], where K is an algebraically closed field of any characteristic.
Gong, SJ, Yu, JT
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A linear preserver problem on maps which are triple derivable at orthogonal pairs [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021 A linear mapping $T$ on a JB$^*$-triple is called triple derivable at orthogonal pairs if for every $a,b,c\in E$ with $a\perp b$ we have $$0 = \{T(a), b,c\} + \{a,T(b),c\}+\{a,b,T(c)\}.$$ We prove that for each bounded linear mapping $T$ on a JB$^*$-algebra $A$ the following assertions are equivalent: $(a)$ $T$ is triple derivable at zero; $(b)$ $T$ is
Ahlem Ben Ali Essaleh +1 more
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