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  2. M568 - Ordered Linear Spaces

M568 - Ordered Linear Spaces

By jsjagajit on Wed, 27/01/2021 - 16:06
Course No
M568
Credit
4
Approval
UG-Elective
Syllabus

Cones and orderings; order convexity; order units; approximate order units; bases. Positive linear mappings and functionals; extension and separation theorems; decomposition of linear functionals into positive linear functionals. Vector lattices; basic theory. Norms and orderings; duality of ordered spaces; (approximate) order unit spaces; base normed spaces. Normed and Banach lattices; AM-spaces, AL-spaces; Kakutani theorems for AM-spaces and ALspaces. Matrix ordered spaces: matricially normed spaces; matricial ordered normed spaces; matrix order unit spaces; Arveson-Hahn-Banach extension theorem.
 

Text Books
1.G.J.O. Jameson, \Lecture Notes in Mathematics" 141 Springer-Verlag,1970.
2. N.C. Wong and K.F. Ng, \(2) Partially ordered topological vector spaces", Oxford University Press, 1973.
3. C.D. Aliprantis and O. Burkinshaw, \Positive operators", Academic Press, 1985.
4. H.H. Schaefer, \Banach lattices and positive operators", Berlin: Springer,1974.
Reference Books

1.W.A. J. Luxemburg and A.C. Zaanen, \Riesz Spaces", Elsevier, 1971.

2. A.C. Zaanen, \Introduction to operator theory in Riesz spces (Vol 1 & Vol 2)", Springer, 1997

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