Common eigenvectors for commutative positive linear operators

Eigenvectors of Order-preserving Linear Operators

Suppose that K is a closed, total cone in a real Banach space X, that A :X!X is a bounded linear operator which maps K into itself, and that A« denotes the Banach space adjoint of A. Assume that r, the spectral radius of A, is positive, and that there exist x ! 1 0 and m& 1 with Am(x ! ) ̄ rmx ! (or, more generally, that there exist x ! a (®K ) and m& 1 with Am(x ! )& rmx ! ). If, in addition, A...

On Eigenvectors of Nilpotent Lie Algebras of Linear Operators

We give a condition ensuring that the operators in a nilpotent Lie algebra of linear operators on a finite dimensional vector space have a common eigenvector. Introduction Throughout this paper V is a vector space of positive dimension over a field f and g is a nilpotent Lie algebra over f of linear operators on V . An element u ∈ V is an eigenvector for S ⊂ g if u is an eigenvector for every o...

3 Spin Operators and Eigenvectors

On some fuzzy positive and linear operators

The purpose of this work is to show that fuzzy Bernstein-Stancu operators introduced in [3] satisfy an A-statistical version of fuzzy Korovkin theorem. Some properties of these operators are also proved. An example of new fuzzy positive and linear operators is presented.

About a class of linear positive operators

In this paper we construct a class of linear positive operators (Lm)m≥1 with the help of some nodes. We study the convergence and we demonstrate the Voronovskaja-type theorem for them. By particularization, we obtain some known operators. 2000 Mathematics Subject Classification: 41A10, 41A25, 41A35, 41A36.