\documentclass[minion]{homework}
\usepackage{cmacros}
\begin{document}
\doclabel{Math 617: Homework 2}
\docdate{Due: February 4, 2012}
\begin{aproblems}
\hproblem\solver{TJ Barry}
 Suppose $p$, $q$ and $r$  belong to  $[1,\infty]$
and that
\[
\frac{1}{p} + \frac{1}{q} + \frac{1}{r} =1,
\]
where $1/\infty = 0$.  Show that if $x,y,z\in \Cplx^n$, then
$$
\sum_{k=1}^n \abs{x_k y_k z_k} \le ||x||_p ||y||_q ||z||_r.
$$

\hproblem \solver{Lymann Gilispie}
Let $Z$ be the set of sequences that are eventually
zero.  Show that if $p\neq q$ then the $\ell_p$ and $\ell_q$ norms
on $Z$ are not equivalent.

\hproblem \solver{Will Mitchell}
Suppose $W$ is an open subspace of the normed vector space $X$.
Show that $W=X$.  Then exhibit an example of a subspace of a 
normed vector space that is not closed.

\hproblem \solver{Vikenty Mikheev}
D\&M 1.30

\hproblem \solver{David Maxwell}
D\&M 1.26

\hproblem \solver{David Maxwell}
D\&M 1.47

\end{aproblems}
\end{document}