Induced map on K theory for certain Γ-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.