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Full-Text Articles in Physical Sciences and Mathematics
K-Theory Of Quadratic Modules: A Study Of Roy's Elementary Orthogonal Group., A. A. Ambily Dr.
K-Theory Of Quadratic Modules: A Study Of Roy's Elementary Orthogonal Group., A. A. Ambily Dr.
Doctoral Theses
This thesis discusses the K-theory of quadratic modules by studying Roys elementary orthogonal group of the quadratic space Q1H(P) over a commutative ring A. We estab- lish a set of commutator relations among the elementary generators of Roys elementary orthogonal group and use this to prove Quillens local-global principle for this elementary group. We also obtain a result on extendability of quadratic modules. We establish nor- mality of the elementary orthogonal group under certain conditions and prove stability results for the Ki group of this orthogonal group. We also prove that Roys elementary orthogonal group and Petrovs odd hyperbolic unitary …
Bures Distance For Completely Positive Maps And Cp-H-Extendable Maps Between Hilbert C*- Modules., Sumesh K Dr.
Bures Distance For Completely Positive Maps And Cp-H-Extendable Maps Between Hilbert C*- Modules., Sumesh K Dr.
Doctoral Theses
Completely positive (CP-) maps are special kinds of positivity preserving maps on C ∗ -algebras. W.F. Stinespring [Sti55] obtained a structure theorem for CP-maps showing that they are closely connected with ∗-homomorphisms. W. Arveson and other operator algebraists quickly realized the importance of these maps. Presently the role of the theory of CP-maps in our understanding of C ∗ -algebras and von Neumann algebras is well recognised. It has been argued by physicists that CPmaps are physically more meaningful than just positive maps due to their stability under ampliations. From quantum probabilistic point of view CP-maps are quantum analogues of …
Proximinality Properties Of Subspaces And Intersection Properties Of Balls In Banach Spaces., Jayanarayanan C. R. Dr.
Proximinality Properties Of Subspaces And Intersection Properties Of Balls In Banach Spaces., Jayanarayanan C. R. Dr.
Doctoral Theses
In this chapter, we explain the background and the main theme of this thesis and provide a chapter-wise summary of its principal results. We introduce some notations and preliminaries that will be used in the subsequent chapters.Study of proximinality related properties and ball intersection related properties of Banach spaces have been an active area of research in the field of geometry of Banach spaces. In this thesis, we mainly study these two classes of Banach space theoretic properties.We consider only Banach spaces over the real field R and all subspaces we consider are assumed to be closed.1.1 PreliminariesFor a Banach …