15 research outputs found
Spectral properties of band irreducible operators
Number of spectral properties of a band irreducible operator on a Banach lattice will be discussed. If is -order continuous, is a pole of the resolvent , and the band E_c^\tilde of all -order continuous functionals on is nonzero, then we prove among others that , that has an eigenvector which is a weak unit, and that the adjoint of has a positive order continuous eigenvector. Furthermore, we provide some criteria of primitivity for band irreducible operators in terms of limits of real sequences. Finally, we discuss the question whether the operator inequalities imply the spectral radius inequality , where is a band irreducible operator on
Spectral properties of band irreducible operators
Number of spectral properties of a band irreducible operator on a Banach lattice will be discussed. If is -order continuous, is a pole of the resolvent , and the band E_c^\tilde of all -order continuous functionals on is nonzero, then we prove among others that , that has an eigenvector which is a weak unit, and that the adjoint of has a positive order continuous eigenvector. Furthermore, we provide some criteria of primitivity for band irreducible operators in terms of limits of real sequences. Finally, we discuss the question whether the operator inequalities imply the spectral radius inequality , where is a band irreducible operator on
Banach limits: Invariance and functional characteristics
Banach limits invariant with respect to the CesA ro transform are studied. New functional characteristics of Banach limits are introduced and studied