Timeline for Norm continuous infinite dimenisonal representation of a Lie group

8 events

when toggle format	what		by	license	comment
Jul 16, 2011 at 16:00	answer	added	paul garrett		timeline score: 2
May 30, 2011 at 20:51	vote	accept	jsb
May 30, 2011 at 12:51	answer	added	Alain Valette		timeline score: 7
May 30, 2011 at 9:12	answer	added	Andrew Stacey		timeline score: 7
May 30, 2011 at 6:46	answer	added	Stefan Waldmann		timeline score: 10
May 30, 2011 at 5:22	comment	added	Robert Israel		In the case $G = \mathbb R$, a one-parameter unitary group is generated by a (possibly unbounded) self-adjoint operator: $\pi(t) = e^{itH}$. This is continuous in the norm topology if and only if the operator $H$ is bounded. This case is indeed of some interest, although in many quantum-mechanics applications $H$ is unbounded.
May 29, 2011 at 22:08	comment	added	Yemon Choi		In many natural examples, the homomorphism will not be continuous if $B(H)$ is given the norm topology. (My intuition is that there are not many interesting examples of locally compact subgroups of $U(H)$ when the latter is given the norm topology, for much the same reason that the unit ball of $B(H)$ is never compact for infinite-dimensonal $H$.)
May 29, 2011 at 20:52	history	asked	jsb	CC BY-SA 3.0