Dunkl--Williams inequality for operators \\ associated with $p$-angular distance

Details Dunkl--Williams inequality for operators \\ associated with $p$-angular distance Dunkl--Williams inequality for operators \\ associated with $p$-angular distance

2010-06-10

arxiv.org/abs/1006.1941v1

Nihonkai Math. J. 21 (2010), no. 1, 11-20

Mathematics

Operator Algebras

11 pages, to appear in Nihonkai Math J

Scientific paper

We present several operator versions of the Dunkl--Williams inequality with respect to the $p$-angular distance for operators. More precisely, we show that if $A, B \in \mathbb{B}(\mathscr{H})$ such that $|A|$ and $|B|$ are invertible, $\frac{1}{r}+\frac{1}{s}=1\,\,(r>1)$ and $p\in\mathbb{R}$, then \begin{equation*} |A|A|^{p-1}-B|B|^{p-1}|^{2} \leq |A|^{p-1}(r|A-B|^{2}+s||A|^{1-p}|B|^{p}-|B||^2)|A|^{p-1}.%\nonumber \end{equation*} In the case that $0

0$, then $$|(U|A|^{p}-V|B|^{p})|A|^{1-p}|^{2}\leq (1+t)|A-B|^{2}+(1+\frac{1}{t})||B|^{p}|A|^{1-p}-|B||^2 \,.$$ We obtain several equivalent conditions, when the case of equalities hold.

Affiliated with

Also associated with

No associations

Rating

Dunkl--Williams inequality for operators \\ associated with $p$-angular distance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dunkl--Williams inequality for operators \\ associated with $p$-angular distance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dunkl--Williams inequality for operators \\ associated with $p$-angular distance will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-490506