From: Michael Orlitzky Date: Wed, 10 Aug 2016 04:19:14 +0000 (-0400) Subject: Add the \dual and \posops commands to mjo-cone. X-Git-Tag: posZ-submitted-laa~21 X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=9e823aa3dcf40f8bfd113476da576fb6b4c0180f;p=mjotex.git Add the \dual and \posops commands to mjo-cone. --- diff --git a/mjo-cone.tex b/mjo-cone.tex index a7507d6..c556f4b 100644 --- a/mjo-cone.tex +++ b/mjo-cone.tex @@ -9,6 +9,10 @@ \input{mjo-common} +% The dual of a subset of an inner-product space; always a closed +% convex cone. +\newcommand*{\dual}[1]{ {#1}^{*} } + % % Common cones. % @@ -27,9 +31,25 @@ % -% Some collections of linear operators +% Some collections of linear operators. % +% The set of all positive operators on its argument. This uses the +% same magic as \boundedops to accept either one or two arguments. If +% one argument is given, the domain and codomain are equal and the +% positive operators fix a subset of that space. When two arguments +% are given, the positive operators send the first argument to a +% subset of the second. +\newcommand*{\posops}[2][]{ + \pi\of{ {#2} + \if\relax\detokenize{#1}\relax + {}% + \else + {,{#1}}% + \fi + } +} + % The set of all S-operators on its argument. \newcommand*{\Sof}[1]{ \mathbf{S} \of{ {#1} } }