https://wiki.devclub.in/index.php?action=history&feed=atom&title=MTL742 2026-04-09T06:03:43Z Revision history for this page on the wiki MediaWiki 1.45.1 https://wiki.devclub.in/index.php?title=MTL742&diff=1640&oldid=prev 2026-03-04T10:14:42Z

<p>Creating course page via bot</p> <p><b>New page</b></p><div>{{Infobox Course<br /> | code = MTL742<br /> | name = Operator Theory<br /> | credits = 3<br /> | credit_structure = 3-0-0<br /> | pre_requisites = MTL411/MTL602<br /> | overlaps = <br /> }}<br /> <br /> == MTL742 : Operator Theory ==<br /> Weak and weak*-topologies, closed convex sets, weak compactness, Alaoglu&#039;s theorem, locally convex topologies, separation of points by linear functionals, Krein-Milman theorem, Stone-Weierstrass theorem. Normed algebras, resolvent, spectrum, spectral radius, functional calculus, spectral mapping theorem, Gelfand&#039;s theory of commutative Banach algebras. Basic properties of compact operators, spectral theory of compact operators, Fredholm alternative, General theory of Schatten-von Neumann classes, Hilbert-Schmidt operators, trace and trace duality in finite dimensions, duality for Schatten-von Neumann classes. Functional calculus for self-adjoint operators, square root of positive operators, polar decomposition, some topologies on B(H), spectral measures, the spectral theorem for normal operators.</div>

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