Abstract:
A lot of studies in operator theory are useful in applications to other disciplines like
engineering and medical sciences among others. One such study is characterization
of properties of operators on Hilbert spaces. A lot of useful results have been
obtained on norms of normal operators. However, characterization of normality
and norm-attainability of these operators have not been exhausted. We outline the
theory of normal, self-adjoint and norm-attainable operators. This study sought
to investigate the conditions for norm-attainability of self-adjoint operators; and
orthogonality of self-adjoint norm-attainable normal operators. The methodology
involved use of inner products, tensor products and some known mathematical
inequalities like Cauchy-Schwarz inequality, parallelogram identity and the
triangle inequality. Results showed a strong relationship between normal operators
and norm-attainable operators’ i.e. normal operators are norm-attainable if they
are self-adjoint. These results are useful in generating quantum bits and estimation
of ground state energies of various molecules like ethane in quantum theory
