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

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.