中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
多复变与复几何学术活动
Some Topics in Several Complex Variables
报告人： Prof. Armen Sergeev （Steklov Mathematical Institute, Moscow）
题 目：Quantum Differentials and Function Spaces
时 间：2019.08.02（星期五）, 16:00-17:00
地 点：数学院南楼N202
摘 要：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 which establishes a correspondence between function spaces and operator algebras in a Hilbert space H. The differential df of a function f (when it is correctly defined) corresponds under this procedure to the commutator of the operator image of f with certain symmetry operator S which is a self-adjoint operator in H with square S2 = I. The image of df under quantization is called the quantum differential of f and is correctly defined even for non-smooth functions f. The arising operator calculus is called, according to Connes, the quantum calculus. In my talk I shall give an interpretation of Schatten ideals of compact operators in a Hilbert space in terms of spaces of functions of one real variable. The main attention is paid to the class of Hilbert–Schmidt operators. The role of the symme- try operator S is played by the Hilbert transform. I shall also consider the function spaces of several real variables. In this case it is possible to define the symmetry operator in terms of Riesz operators and Dirac matrices.
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