Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reverse triangle inequality in Hilbert $C^*$-modules   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
$<e_i,e_j>=0 (1\leq i\neq j \leq m)$ 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 .

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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: econ