Titlebook: An Introduction to C*-Algebras and Noncommutative Geometry; Heath Emerson Textbook 2024 Springer Nature Switzerland AG 2024 C*-algebras.K-

协定

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

恫吓

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

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

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

宣称

暴发户

CHOIR

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

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.