Abstract
Abstract This chapter introduces an elementary theory of C*-algebras in the context of Bishop-style constructive mathematics. It givens proof of the Gelfand-Naĭmark-Segal (GNS) construction theorem in Bishop's constructive mathematics. This important theorem in the theory of operator algebras says that for each C*-algebra and every state, there exists a cyclic representation on some Hilbert space. This chapter's contribution is of particular interest in view of the Bridges-Hellman debate on whether constructive mathematics is able to cope with quantum mechanics. Since quantum mechanics is bound up with the theory of operator algebras on Hilbert spaces, a constructive treatment of the latter has been a challenge for constructive mathematics from the very beginning.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
