Norm Estimates of the Partial Transpose Map on the Tensor Products of Matrices

Norm Estimates of the Partial Transpose Map on the Tensor Products of Matrices We present a norm estimate for the partial transpose map Θ on the tensor product $$M_m \otimes M_n$$ $$\Theta \left( \sum_k A_k \otimes B_k \right) := \sum_k A_k \otimes B_k^T$$ with respect to a unitarily invariant norm. This is related to the norm estimates of the following maps on M m,n in terms of the spectral norm of $$\displaystyle \sum_k A_k \otimes B_k$$ : $$X \longmapsto \sum_k A_k X B_k \quad \textrm{and} \quad X \longmapsto \sum_k A_k X B_k^T.$$ We show further that in the special case of $$A \otimes I_n + I_m \otimes B$$ as well as AX + XB and AX + XB T those estimates are much improved and that $$\| A \otimes I_n + I_m \otimes B^T \|_p = \| A \otimes I_n + I_m \otimes B \|_p$$ for certain Schatten p-norms. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Norm Estimates of the Partial Transpose Map on the Tensor Products of Matrices

, Volume 12 (1) – Oct 29, 2007
16 pages

/lp/springer_journal/norm-estimates-of-the-partial-transpose-map-on-the-tensor-products-of-JU0QXlOxkM
Publisher
Birkhäuser-Verlag
Copyright © 2007 by Birkhäuser Verlag Basel/Switzerland
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-007-2121-7
Publisher site
See Article on Publisher Site

You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month Explore the DeepDyve Library Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. Organize your research It’s easy to organize your research with our built-in tools. Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. Monthly Plan • Read unlimited articles • Personalized recommendations • No expiration • Print 20 pages per month • 20% off on PDF purchases • Organize your research • Get updates on your journals and topic searches$49/month

14-day Free Trial

Best Deal — 39% off

Annual Plan

• All the features of the Professional Plan, but for 39% off!
• Billed annually
• No expiration
• For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588$360/year

billed annually

14-day Free Trial