Document Type
Thesis
Date of Award
9-30-1985
Degree Name
Master of Science in Applied Mathematics - (M.S.)
Department
Mathematics
First Advisor
Vladislav V. Goldberg
Second Advisor
Ronald Gautreau
Third Advisor
Denis L. Blackmore
Abstract
Everyone is familiar with the imaginary unit. Its square is minus one and it has a conjugate equal to the negative of itself. The imaginary unit is a conjugate operator. One can also simply define an operator whose square is plus one, with a distinct conjugate operation again returning the negative of itself. Thus one obtains a second conjugate operator. If the product of these two operators is taken, a third conjugate operator with distinct properties is obtained. These three conjugate operators together with the real number 1 form a "conjugate basis" for the spaces that will be developed here. These spaces will consist of linear combinations of these four operators. In standard rectangular form, the coefficients of the linear combinations will, by definition, have no conjugate transformations. The coefficients will thus be Hermitian operators. The requirement that the 'magnitude' defined on an operator space be a real number and derived as a product of conjugates will then place important restrictions on the forms of the linear combinations considered.
Recommended Citation
Palko, Ronald Stephen, "Conjugate operators and operator spaces" (1985). Theses. 3462.
https://digitalcommons.njit.edu/theses/3462
