TY - BOOK AU - Kumar,Manish TI - C∗-extreme Maps and Nest Algebras U1 - 512.55 23 PY - 2022/// CY - Bangalore PB - Indian Statistical Institute KW - Algebras KW - Nest Algebras KW - C∗-algebras KW - C∗-extreme Maps KW - Logmodular Algebras N1 - Thesis (Ph.D.) - Indian Statistical Institute, 2022; Includes bibliographical references and index; Introduction -- 1 Preliminaries -- 1.1 C∗-algebras -- 1.2 Completely positive maps -- 1.3 Positive operator valued measures -- 1.4 Correspondence between CP maps and POVMs -- 1.5 Nest algebras and factorization property -- 2 C∗-convexity Structure of Generalized State Spaces -- 2.1 Definitions and general properties -- 2.2 Abstract characterizations of C∗-extreme maps -- 2.3 Direct sums of pure UCP maps -- 2.4 Krein-Milman type theorem for UCP maps on separable C∗-algebras 2.5 Examples and applications -- 3 Normal C∗-extreme Maps -- 3.1 Normal C∗-extreme maps on type I factors -- 3.2 Krein-Milman type theorem for UCP maps on type I factors -- 3.3 Examples of normal C∗-extreme maps -- 4 C∗-extreme Positive Operator Valued Measures -- 4.1 General Properties of C∗-extreme POVMs -- 4.2 C∗-extreme POVMs with commutative ranges -- 4.3 Atomic C∗-extreme POVMs -- 4.4 Singular POVMs and their direct sums -- 4.5 Measure Isomorphic POVMs -- 5 C∗-extreme Maps on Commutative C∗-algebras -- 5.1 Regular atomic and non-atomic POVMs -- 5.2 Regular C∗-extreme POVMs -- 5.3 Krein-Milman type theorem for PH(X) -- 5.4 Applications to UCP Maps on C(X) -- 6 Logmodular Algebras -- 6.1 Definitions and examples -- 6.2 Lattices of logmodular algebras -- 6.3 Proof of the main result -- 6.4 Reflexivity of algebras with factorization -- Open Problems; Guided by Prof. B. V. Rajarama Bhat UR - http://dspace.isical.ac.in:8080/jspui/handle/10263/7244 ER -