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University</title></head><body>
<div>The following QIP seminar, which will take place on Tuesday
September 20 at 14:00 hours in 509 Lake Hall (Northeastern
University), may be of interest to the readers of this list.</div>
<div><br></div>
<hr>
<div align="center"><font size="+2">Norm Compression Inequalities for
Block Matrices</font></div>
<div align="center"><font size="+1">(<i>Northeastern University's
Probability, Statistics and Applications Seminar</i>)</font></div>
<div align="center"><br></div>
<div align="center"><font size="+1"><i>by</i> Koenraad Audenaert
(<i>Imperial College London</i>)</font></div>
<div align="center"><br></div>
<div align="center"><u>ABSTRACT</u></div>
<div><br></div>
<blockquote>I consider inequalities for the Schatten q-norms, which
are non-commutative generalistions of the l_q norms. Given a block
partitioned matrix, one can try and bound the q-norm of the matrix
itself in terms of the q-norms of the blocks. The inequalities that
arise can be called norm compression inequalities, because the bound
is stated in terms of the elements of the norm compression of the
matrix, which is what you get when replacing every block of the matrix
by its norm. In this talk I give an overview of previously known
bounds of this kind. I then present some norm compression bounds for
positive semidefinite 2X2 block matrices, complementing earlier work
by Chris King. Finally, I give an overview of various conjectured norm
compression inequalities, and discuss some of the implications their
validity would have in quantum information theory.</blockquote>
<blockquote> </blockquote>
<blockquote>See also math.FA/0505680</blockquote>
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