C*-algebra: Banach-algebra with involution * + ||a*a||=||a||². Gelfand-Naimark-Segal: every C*-algebra embeds in B(H) for some Hilbert H. Foundation of operator-algebraic QM + non-commutative-geometry.
C*-algebra: Banach-algebra with involution * + ||a*a||=||a||². Gelfand-Naimark-Segal: every C*-algebra embeds in B(H) for some Hilbert H. Foundation of operator-algebraic QM + non-commutative-geometry.