From 9e823aa3dcf40f8bfd113476da576fb6b4c0180f Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Wed, 10 Aug 2016 00:19:14 -0400
Subject: [PATCH] Add the \dual and \posops commands to mjo-cone.

---
 mjo-cone.tex | 22 +++++++++++++++++++++-
 1 file changed, 21 insertions(+), 1 deletion(-)

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} } }
 
-- 
2.43.2