Norm preserver maps of Jordan product on the algebra Mn of n×n complex matrices are studied, with respect to various norms. A description of such surjective maps with respect to the Frobenius norm is obtained: Up to a suitable scaling and unitary similarity, they are given by one of the four standard maps (identity, transposition, complex conjugation, and conjugate transposition) on Mn, except ...

for $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...

In this paper we study Jordan-structure-preserving perturbations of matrices selfadjoint in the indefinite inner product. The main result of the paper is Lipschitz stability of the corresponding similitude matrices. The result can be reformulated as Lipschitz stability, under small perturbations, of canonical Jordan bases (i.e., eigenvectors and generalized eigenvectors enjoying a certain flipp...

Let B(X ) be the algebra of all bounded linear operators on a complex Banach space X and let I(X ) be the set of non-zero idempotent operators in B(X ). A surjective map φ : B(X ) → B(X ) preserves nonzero idempotency of the Jordan products of two operators if for every pair A, B ∈ B(X ), the relation AB + BA ∈ I(X ) implies φ(A)φ(B) + φ(B)φ(A) ∈ I(X ). In this paper, the structures of linear s...