C*-algebraic methods in spectral theory
Contact:
Serge Richard (richard@math.nagoya-u.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
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Class dates :
April 13, 20, 27
May 11, 18, 25
June 1, 8, 15, 22, 29
July 6, 13, 20, 27
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Students reports :
Convergence in weak / strong topology, by Renta Yagi
Example of an unbounded operator, and self-adjoint 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 non-unital 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
G-space and the action on Co-functions, 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 non-commutative geometry: algebraic topology (personal notes), by Wang Yibin
On the spectral radius, by Nakanishi Kenta
On the irrational rotation algebra, by Nakashima Kensuke
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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, 1215-1232.
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[DG13] E.B. Davies, V. Georgescu, C*-algebras associated with some second order differential operators, J. Operator Theory 70 (2013), no. 2, 437-450.
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[GI06] V. Georgescu, A. Iftimovici, Localizations at infinity and essential spectrum of quantum Hamiltonians I: General theory, Rev. Math. Phys. 18 (2006), no. 4, 417-483.
[LMR10] M. Lein, M. Mantoiu, S. Richard,
Magnetic pseudodifferential operators with coefficients in C*-algebras, Publ. Res. Inst. Math. Sci. 46 (2010), no. 4, 755-788.
[Man02] M. Mantoiu, C*-algebras, dynamical systems at infinity and the essential spectrum of generalized Schroedinger operators, J. Reine Angew. Math. 550 (2002), 211-229.
[Man013] M. Mantoiu, On the essential spectrum of phase-space anisotropic pseudodifferential operators, Math. Proc. Cambridge Philos. Soc. 154 (2013), no. 1, 29-39.
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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, 137-172, Theta Ser. Adv. Math., 5, Theta, Bucharest, 2005.
[MPR07] M. Mantoiu, R. Purice, S. Richard, Spectral and propagation results for magnetic Schroedinger operators; a C*-algebraic framework, J. Funct. Anal. 250 (2007), no. 1, 42-67.
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products of C*-algebras, Math. Proc. Camb. Phyl. Soc. 106, 293-311, 1989.
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crossed products of C*-algebras II, Math. Ann. 287, 595-612, 1990.
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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, 73-111.
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[Tes09] G. Teschl, Mathematical methods in quantum mechanics, with applications to Schroedinger operators, Graduate Studies in Mathematics 99, American Mathematical Society, Providence, RI, 2009.
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[Wil07] D.P. Williams, Crossed products of C*-algebras, Mathematical Surveys and Monographs, 134. American Mathematical Society, Providence, RI, 2007.
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