Weak Containment and Amenability

Rongwei Yang
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Rongwei Yang: University at Albany, the State University of New York, Department of Mathematics & Statistics

Chapter Chapter 9 in A Spectral Theory Of Noncommuting Operators, 2024, pp 213-233 from Springer

Abstract: Abstract This chapter extends the discussion in Chap. 2 to finitely generated groups. We assume throughout this chapter that the Hilbert space ℋ $${\mathcal H}$$ has infinite dimension. In this case, Kuiper’s theorem [148] asserts that the group of unitaries U ( ℋ ) $$U({\mathcal H})$$ is contractible. Recall that given two unitary representations ( π , ℋ ) $$(\pi , {\mathcal H})$$ and ( ρ , ℋ ) $$(\rho , {\mathcal H})$$ of a group G, we say that π $$\pi $$ contains ρ $$\rho $$ and write ρ

Date: 2024
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DOI: 10.1007/978-3-031-51605-4_9

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