ABSTRACT
Completely positive maps is an important eld due to its signicance,
application and mathematics itself. While discussing the properties of the
positive maps, researchers have questioned whether the properties of the
positive maps also hold for completely positive maps. In chapter 1, we
have started with a C-algebra A, generated on A other C-algebras and
then investigated these forms of C-algebras. We investigated whether
the properties of A such as self-adjointedness and completeness under
norm still hold on the C-algebras generated on A. In chapter 2, the condition
for the positivity of the elements of these generated C-algebras
is given. This has been done by showing that their inner product with
elements from a Hilbert space is positive. A unital contraction is necessarily
positive. Conditions under which positive maps are completely
positive are discussed. In chapter 3, boundedness and complete boundedness
of these maps have been investigated. This, we have done by
showing that, indeed, whenever the operator system is a C-algebra, then
a positive map is bounded and completely bounded, if its norm is equal
to its complete bound which must be nite. All completely positive maps
are completely bounded, however the converse is not always true. This
has been shown by giving examples and counter examples. The results
of this study will pave way for construction of new C-algebras from the
known ones, which will be helpful in the development of the research on
positive maps on these generated C-algebras and may also be applied by
mathematicians in solving spectral problems.
Owino, J (2021). On Completely Positive Maps. Afribary. Retrieved from https://track.afribary.com/works/on-completely-positive-maps
Owino, Julia "On Completely Positive Maps" Afribary. Afribary, 06 May. 2021, https://track.afribary.com/works/on-completely-positive-maps. Accessed 27 Nov. 2024.
Owino, Julia . "On Completely Positive Maps". Afribary, Afribary, 06 May. 2021. Web. 27 Nov. 2024. < https://track.afribary.com/works/on-completely-positive-maps >.
Owino, Julia . "On Completely Positive Maps" Afribary (2021). Accessed November 27, 2024. https://track.afribary.com/works/on-completely-positive-maps