Kasprove’s Stabilization and Fredholm Generalized Index Theory

Lunchuan Zhang
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Lunchuan Zhang: Renmin University of China, School of Mathematics

Chapter Chapter 2 in Hilbert C*- Modules and Quantum Markov Semigroups, 2024, pp 69-129 from Springer

Abstract: Abstract In this chapter, we show that every countably generated Hilbert A-module can be regarded as a complemented submodule of H ⊗ A $$H\otimes A$$ (in the sense of unitary equivalence), where H is a separable Hilbert space. This is one of the fundamental results of Hilbert C ∗ $$C^*$$ -module theory, which is called Kasprove’s stabilization theorem.

Date: 2024
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DOI: 10.1007/978-981-99-8668-2_2

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