协定
发表于 2025-3-25 06:25:00
The Index Theorem of Atiyah and Singer,The elliptic operator . acting on the circle . has a discrete spectrum of the integers. In particular, the dimensions of the kernels of the continuously varying family of operators ., for ., jump discontinuously as . crosses an integer point.
领带
发表于 2025-3-25 10:29:47
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恫吓
发表于 2025-3-25 13:34:04
https://doi.org/10.1007/978-1-349-19012-6 (Definition 1.1.7) is due to Gelfand in around 1943. The term “C*-algebra” is due to I.E. Segal in 1947, who used it to describe norm-closed *-subalgebras of bounded operators on a Hilbert space; the “C” stands for “closed.”
移植
发表于 2025-3-25 18:16:33
https://doi.org/10.1007/978-1-349-08655-9of view are unimportant, they are locally homotopic to line segments, but the . properties of the curves can effect values of line integrals, and looking at the ensemble of all curves up to homotopy reveals topological properties of the region.
idiopathic
发表于 2025-3-25 20:36:23
https://doi.org/10.1007/978-1-349-08655-9e Bott Periodicity phenomenon of topological K-theory, while algebraic K-theory does not, so the two differ in their treatment of higher K-groups. Operator K-theory is Morita invariant, and is the correct homology theory for studying the “noncommutative spaces” of Noncommutative Geometry.
放牧
发表于 2025-3-26 00:35:19
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宣称
发表于 2025-3-26 04:40:31
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暴发户
发表于 2025-3-26 08:40:31
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CHOIR
发表于 2025-3-26 16:02:38
K-Theory for C*-Algebras,e Bott Periodicity phenomenon of topological K-theory, while algebraic K-theory does not, so the two differ in their treatment of higher K-groups. Operator K-theory is Morita invariant, and is the correct homology theory for studying the “noncommutative spaces” of Noncommutative Geometry.
lambaste
发表于 2025-3-26 18:40:11
An Introduction to KK-Theory,atic approach to the intersection product (the composition operation in the category KK) and produced applications to families and foliation index theorems. The article (Baaj and Julg (C R Acad Sci Paris Sér I Math 296(21):875–878, 1983)) gives an important description of KK-theory in terms of unbounded operators.