Commutants and spectral properties of operators in hilbert spaces
Abstract
This thesis is devoted to the study of commutants and spectral properties of
operators in Hilbert spaces. This is done via the following operator equations:
AB =λBA, where λ ∈ℂ, AX = XB and AXB = X. In the operator equation
AB = λ BA, conditions on A and B under which λ =1 are investigated. This
indeed is a sufficient condition for the operators A and B to belong to the
commutant of each other. In the operator equations AX = XB and AXB = X ,
conditions that ensure the existence of the operator equations C(A,B)X = 0 and
R(A, B)X = 0 are given. Finally in the operator equation AB = λ BA, the equality
of the general spectra and other subsets of the spectra namely essential and
approximate point spectra of AB and BA or B and λ B, are established. This
final bit justifies the spectral properties part of our thesis
Sponsorhip
University of NairobiPublisher
School of mathematics