usepackage{graphics,epsfig,epstopdf}
usepackage{amsmath,amssymb,psfrag,mathtools}
usepackage{amsthm}
usepackage{cite}
usepackage{mleftright}
usepackage{tikz}
newcommand{lla}{langlelangle}
newcommand{rra}{ranglerangle}
DeclarePairedDelimiter{norm}{lVert}{rVert}
newcommand*circled[1]{tikz[baseline=(char.base)]{
            node[shape=circle,draw,inner sep=1pt] (char) {#1};}}

newtheorem{theorem}{Theorem}
newtheorem{corollary}{Corollary}[theorem]
newtheorem{lemma}[theorem]{Lemma}
newtheorem{remark}{Remark}
newtheorem{proposition}{Proposition}