Timeline for A question in functional analysis about selfadjoint operator

5 events

when toggle format	what		by	license	comment
Jan 13 at 3:26	vote	accept	luyao
Jan 12 at 19:17	comment	added	Iosif Pinelis		@GiorgioMetafune : Thank you for this nice comment.
Jan 12 at 18:40	comment	added	Giorgio Metafune		This is another proof: if $T$ is positive, $(Tx,x) \leq c (x,x) $ is equivalent to $\\|T^{1/2}x\\|^2 \leq c\\|x\\|^2$ or $\\|y\\|^2 \leq c \\|T^{-1/2}y\\|^2$ which is $(T^{-1}y,y) \geq c^{-1}(y,y)$. In the general case $0 \leq T \leq S$ is equivalent to $S^{-1/2} TS^{-1/2} \leq I$ which, by the previous case, gives $S^{1/2} T^{-1}S^{1/2} \geq I$ or $T^{-1} \geq S^{-1}$.
Jan 12 at 17:37	history	edited	Iosif Pinelis	CC BY-SA 4.0	added 320 characters in body
Jan 12 at 17:14	history	answered	Iosif Pinelis	CC BY-SA 4.0