C*algebraic methods in spectral theory
Contact:
Serge Richard (richard@math.nagoyau.ac.jp), Rm. 247 in Sci. Bldg. A
Registration code : 3211087
Lecturer : Serge Richard
Schedule : Wednesday (8.45  10.15) in room 309 of the math building, and on Zoom

Class dates :
April 13, 20, 27
May 11, 18, 25
June 1, 8, 15, 22, 29
July 6, 13, 20, 27

Students reports :
Convergence in weak / strong topology, by Renta Yagi
Example of an unbounded operator, and selfadjoint operators are closed, by Renta Yagi
Natural closure of densely defined bounded operators, by Huyga Ito
Spectral radius and norm in a C*algebra, by Huyga Ito
Example of a nonunital Abelian Banach algebra, by Huyga Ito
Spectrum and spectral support, by Huyga Ito
On double centralizers, by Huyga Ito
Various topologies, by Huyga Ito
Spectrum and eigenvalues of bounded multiplication operators, by Ayumi Ukai
About Gelfand transform, and 3 equalities with the Haar measure, by Renta Yagi
On the compactness of the unit ball in the w*topology, by Ryotaro Fushimi
On the quotient of a group by a normal subgroup, by Ryotaro Fushimi
Neumann series and the inverse map, by Ryotaro Fushimi
Gspace and the action on Cofunctions, by Ryotaro Fushimi
Spectrum of multiplication operators, by Huyga Ito
About the Fourier transform, by Huyga Ito
Operators and observables affiliated to a C*algebra, by Ayumi Ukai
Various exercises from the lecture notes, by Shuto Shimizu
Orthogonality in Hilbert spaces, by Nakanishi Kenta
Weyl calculus and magnetic calculus, by Shuto Shimizu
Introduction to noncommutative geometry: algebraic topology (personal notes), by Wang Yibin
On the spectral radius, by Nakanishi Kenta
On the irrational rotation algebra, by Nakashima Kensuke

References : (electronic version available upon request)
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[AMP02] W.O. Amrein, M. Mantoiu, R. Purice, Propagation properties for Schroedinger operators affiliated with certain C*algebras, Ann. Henri Poincaré 3 (2002), no. 6, 12151232.
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[LMR10] M. Lein, M. Mantoiu, S. Richard,
Magnetic pseudodifferential operators with coefficients in C*algebras, Publ. Res. Inst. Math. Sci. 46 (2010), no. 4, 755788.
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[MPR05] M. Mantoiu, R. Purice, S. Richard, Twisted crossed products and magnetic pseudodifferential operators, in Advances in operator algebras and mathematical physics, 137172, Theta Ser. Adv. Math., 5, Theta, Bucharest, 2005.
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[Ric05] S. Richard, Spectral and scattering theory for Schroedinger operators with Cartesian anisotropy, Publ. Res. Inst. Math. Sci. 41 (2005), no. 1, 73111.
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