# Induced map on $K$-theory for certain $\Gamma$-equivariant maps between Hilbert spaces

### Tsuyoshi Kato

Kyoto University, Japan

## Abstract

Higson–Kasparov–Trout introduced an infinite-dimensional Clifford algebra of a Hilbert space, and verified Bott periodicity on $K$-theory. To develop an algebraic topology of maps between Hilbert spaces, in this paper we introduce an induced Hilbert Clifford algebra and construct an induced map between $K$-theory of the Higson–Kasparov–Trout Clifford algebra and the induced Clifford algebra. We also compute its $K$-group for some concrete case.

## Cite this article

Tsuyoshi Kato, Induced map on $K$-theory for certain $\Gamma$-equivariant maps between Hilbert spaces. J. Noncommut. Geom. 15 (2021), no. 4, pp. 1433–1467

DOI 10.4171/JNCG/442