| dc.description.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 | en |
