We extend the notion spin norm slightly to a real reductive Lie group G in the Harish-Chandra class.Let K be a maximal compact subgroup of G.In this setting, the spin norm of any K -type is still bounded from below by its lambda norm.We establish a bijection between irreducible tempered ( g, K )modules with nonzero Dirac cohomology and those K -types whose spin norm equals their lambda norm.
Ding et al. (Fri,) studied this question.