Reverse triangle inequality in Hilbert $C^*$-modules

Details Reverse triangle inequality in Hilbert $C^*$-modules Reverse triangle inequality in Hilbert $C^*$-modules

2009-11-14

arxiv.org/abs/0911.2751v1

J. Inequal. Pure Appl. Math. 10 (2009), no. 4, art. 110

Mathematics

Functional Analysis

12 Pages; to appear in J. Inequal. Pure Appl. Math (JIPAM)

Scientific paper

We prove several versions of reverse triangle inequality in Hilbert $C^*$-modules. We show that if $e_1, ..., e_m$ are vectors in a Hilbert module ${\mathfrak X}$ over a $C^*$-algebra ${\mathfrak A}$ with unit 1 such that $=0 (1\leq i\neq j \leq m)$ and $\|e_i\|=1 (1\leq i\leq m)$, and also $r_k,\rho_k\in\Bbb{R} (1\leq k\leq m)$ and $x_1, ..., x_n\in {\mathfrak X}$ satisfy $$0\leq r_k^2 \|x_j\|\leq {Re}< r_ke_k,x_j> ,\quad0\leq \rho_k^2 \|x_j\| \leq {Im}< \rho_ke_k,x_j> ,$$ then [\sum_{k=1}^m(r_k^2+\rho_k^2)]^{{1/2}}\sum_{j=1}^n \|x_j\|\leq\|\sum_{j=1}^nx_j\|, and the equality holds if and only if \sum_{j=1}^n x_j=\sum_{j=1}^n\|x_j\|\sum_{k=1}^m(r_k+i\rho_k)e_k .

Affiliated with

Also associated with

No associations

Rating

Reverse triangle inequality in Hilbert $C^*$-modules 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 Reverse triangle inequality in Hilbert $C^*$-modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reverse triangle inequality in Hilbert $C^*$-modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-113517