109 lines
3.0 KiB
TeX
109 lines
3.0 KiB
TeX
% tensor products
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\newcommand{\thk}{\cH\otimes\cK}
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\newcommand{\amb}{\bA \otimes_{\max} \bB}
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\newcommand{\omax}{\otimes_{\max}}
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\newcommand{\omin}{\otimes_{\min}}
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\newcommand{\ovn}{\overline{\otimes}}
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% probability
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\newcommand{\PS}{(\Omega,\cM,\cP)}
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\newcommand{\rvf}{f:\Omega \to \bR}
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\newcommand{\linf}{\cL^{\infty -}\PS}
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\newcommand{\probc}{\text{Prob}_c(\bR)}
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\newcommand{\prob}{\text{Prob}(\bR)}
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% maps
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\newcommand{\into}{\hookrightarrow}
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\newcommand{\onto}{\twoheadrightarrow}
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\newcommand{\act}{\curvearrowright}
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\newcommand{\ee}{\varepsilon}
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\newcommand{\sm}{\setminus}
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\newcommand{\Om}{\Omega}
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\newcommand{\simi}{\sim_{\infty}}
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%limits
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\newcommand{\limsupn}{\underset{n}{\text{limsup}}}
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\newcommand{\sotc}{\stackrel{\text{SOT}}{\to}}
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\newcommand{\wotc}{\stackrel{\text{WOT}}{\to}}
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\newcommand{\sotlim}{\text{SOT-}\lim}
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\newcommand{\wotlim}{\text{WOT-}\lim}
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% useful for nuclear, lifting maps, etc....
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\newcommand{\tphi}{\tilde{\phi}}
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\newcommand{\tpsi}{\tilde{\psi}}
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\newcommand{\hphi}{\hat{\phi}}
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\newcommand{\hpsi}{\hat{\psi}}
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\newcommand{\phil}{\phi_\lambda}
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\newcommand{\psil}{\psi_\lambda}
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\newcommand{\mkl}{M_{k(\lambda)}}
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\newcommand{\mkn}{M_{k(n)}}
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\newcommand{\phin}{\phi_n}
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\newcommand{\psin}{\psi_n}
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\newcommand{\vphi}{\varphi}
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\newcommand{\floor}[1]{\lfloor #1 \rfloor}
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\newcommand{\supp}{\text{supp}}
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\newcommand{\wk}{\text{wk}}
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\newcommand{\Tr}{\text{Tr}}
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\newcommand{\dist}{\text{dist}}
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\newcommand{\rank}{\text{rank}}
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\newcommand{\sgn}{\text{sgn}}
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\newcommand{\ev}{\text{ev}}
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\newcommand{\spr}{\text{spr}}
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\newcommand{\tD}{\tilde{\Delta}}
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\newcommand{\uv}{\underline}
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\newcommand{\tr}{\text{tr}}
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\newcommand{\id}{\text{id}}
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\newcommand{\ad}{\text{ad}}
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\newcommand{\Ad}{\text{Ad}}
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\newcommand*{\tc}[2]{(\ov{#1}^{#2},#2)}
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% Types for von Neumann algebras
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\newcommand{\I}{\text{I}}
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\newcommand{\II}{\text{II}}
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\newcommand{\III}{\text{III}}
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\newcommand{\IIIl}{\text{III}_{\lambda}}
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% note the last character of this last one is an "ell", its just that my font has capital i and lower-case l being the same character.....
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%operators
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% basic algebra
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\DeclareMathOperator{\Ann}{Ann}
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\DeclareMathOperator{\Hom}{Hom}
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\DeclareMathOperator{\End}{End}
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\DeclareMathOperator{\Aut}{Aut}
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\DeclareMathOperator{\im}{im}
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% K-theory and regularity for C*-algebras
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\DeclareMathOperator{\Ell}{Ell}
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\DeclareMathOperator{\Aff}{Aff}
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\DeclareMathOperator{\KT}{KT}
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\DeclareMathOperator{\Cu}{Cu}
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\DeclareMathOperator{\ka}{K^{\text{alg}}}
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\DeclareMathOperator{\ku}{K^\text{alg,u}}
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\DeclareMathOperator{\hka}{\ov{K}_1^{\text{alg}}}
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\DeclareMathOperator{\hku}{\ov{K}_1^{\text{alg,u}}}
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\newcommand{\MvN}{\sim_{\text{MvN}}}
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% exponential rank and length for C*-algebras
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\newcommand{\cer}{\text{cer}}
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\newcommand{\cel}{\text{cel}}
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% KK-theory and Ext
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\DeclareMathOperator{\KK}{KK}
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\DeclareMathOperator{\KKn}{KK_{\text{nuc}}}
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\DeclareMathOperator{\KKs}{KK_{\text{sep}}}
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\DeclareMathOperator{\Ext}{Ext}
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\DeclareMathOperator{\Extn}{Ext_{\text{nuc}}}
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% direct/inverse limits
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\newcommand{\dlim}{\underset{\to}{\lim}}
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\newcommand{\ilim}{\underset{\leftarrow}{\lim}}
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