Linear Preserver Problems

Some General Techniques on Linear Preserver Problems

Several general techniques on linear preserver problems are described. The first one is based on a transfer principle in Model Theoretic Algebra that allows one to extend linear preserver results on complex matrices to matrices over other algebraically closed fields of characteristic 0. The second one concerns the use of some simple geometric technique to reduce linear preserver problems to sta...

Some Linear Preserver Problems on B(h) concerning Rank and Corank

As a continuation of the work on linear maps between operator algebras which preserve certain subsets of operators with finite rank, or finite corank, here we consider the problem inbetween, that is, we treat the question of preserving operators with infinite rank and infinite corank. Since, as it turns out, in this generality our preservers cannot be written in a nice form what we have got use...

Ela Euclidean and Circum-euclidean Distance Matrices: Characterizations and Linear Preservers

Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.

A Survey of Invertibility and Spectrum Preserving Linear Maps

. FA ] 4 J ul 1 99 7 DIAMETER PRESERVING LINEAR BIJECTIONS OF C ( X )

The aim of this paper is to solve a linear preserver problem on the function algebra C(X). We show that in case X is a first countable compact Hausdorff space, every linear bijection φ : C(X) → C(X) having the property that diam(φ(f)(X)) = diam(f(X)) (f ∈ C(X)) is of the form φ(f) = τ · f ◦ φ+ t(f)1 (f ∈ C(X)) where τ ∈ C, |τ | = 1, φ : X → X is a homeomorphism and t : C(X) → C is a linear func...