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Conference «Contemporary Mathematics and its applications» dedicated to the results of research supported by the Russian Science Foundation grant 14-50-00005
November 19, 2018 11:30–11:50, Direction "Real and complex analysis and its applications", Moscow, Steklov Mathematical Institute of RAS, Conference Hall (8 Gubkina)
 


Quantum Calculus and Schatten Ideals

A. G. Sergeev
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MP4 242.2 Mb

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A. G. Sergeev
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Abstract: One of the goals of noncommutative geometry is the translation of basic notions of analysis into the language of Banach algebras. This translation is done using the quantization procedure. The arising operator calculus is called, following Connes, the quantum calculus. In our talk we shall give several assertions from this calculus concerning the interpretation of Schatten ideals of compact operators in a Hilbert space in terms of function theory. The main attention is paid to the case of Hilbert{ Schmidt operators.

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