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We study lower bounds on the number of nonzero entries in (0 , 1) matrices such that the permanent is always convertible to the determinant by placing ± signs on matrix entries. [ABSTRACT FROM AUTHOR]

We study the maps that transform one immanant into another. No surjectivity or linearity is imposed; the rudiments of the former are weakly embedded into the functional equation via {ie874-01}. We show that this property alone implies that Φ is linear and bijective. [ABSTRACT FROM AUTHOR]

Abstract: Let be a field and . Suppose contain all rank-one idempotents. The structure of surjections satisfying is determined. Similar results are also obtained for (a) subsets of bounded operators acting on a complex or real Banach space , (b) the space of Hermitian matrices acting on n-dimensional vectors over a skew-field , (c) subsets of self-adjoint bounded linear operators acting on an infinite dimensional complex Hilbert space. It is then illustrated that the results can be applied to characterize mappings ϕ on matrices or operators such thatfor functions F such as the spectral norm, Schatten p-norm, numerical radius and numerical range, etc. [Copyright &y& Elsevier]

A complete characterization of additive mappings Φ : ℬ( $${\fancyscript X}$$ ) → ℬ( $${\fancyscript Y}$$ ), which map rank–one idempotents to themselves or to zero, is given. [ABSTRACT FROM AUTHOR]