The Department of Mathematical and Computational Sciences at the National Institute of Technology, Karnataka will conduct a workshop on Functional Analysis and Operator Algebras from 2nd to 7th June 2014.
Topics covered: Functional Analysis - Banach spaces; Hahn-Banach theorems; Open mapping theorem; Closed graph theorem; Uniform boundedness principle; Dual space; Weak topology; Second dual and the weak*-topology; Reflexive space; Arzela-Ascoli theorem; Banach-Alaoglu theorem; Banach-Mazur theorem; Topologies on the space of bounded operators; Compact operators. Hilbert spaces; Orthonormal basis; Orthogonal complement; Gram-Schmidt process; Parseval's identity; Projection theorem; Riesz representation theorem; Adjoint operators; Self-adjoint, normal, unitary operators; Spectral theorem; Projections; Invariant and reducing subspaces.
Operator Algebras : Banach algebras and invertible group; Regular and singular elements; Topological divisors of zero; Spectrum; Radical; Semi-simplicity; Multiplicative linear functionals; Gelfand transform and applications; Gelfand-Mazur theorem; Maximal ideal spaces; Non-trivial Banach algebras. C*-Algebras; Commutative C*-Algebras; Spectral theorem and applications; Polar decomposition; Positive linear functionals and states; GNS construction; Non-unital C*-Algebras; von-Neumann Algebra.
Additional Topics in Functional Analysis : Geometry of Banach spaces; Approximation theory; Fixed point theory; Inverse Problems; Hyers-Ulam stability (Functional Equations).
Eligibility: M.Sc./M.Phil./Ph.D Students, College/University Teachers and those who are interested to do research in Functional Analysis/Operator Theory/Operator Algebras
There is no registration fee. Participants shall be offered free accommodation in campus hostels/guest houses (shared if necessary), to be arranged on request.
To participate in the workshop, fill in the application form which can be downloaded from the official website and send the scanned copy of the filled form to email@example.com. List of selected participants will be informed by email on 13.05.2014.
Last date of receipt of application : 12.05.2014
All further details can be obtained in the official website of NITK, http://faoa2014.nitk.ac.in/