Banach envelopes in symmetric spaces of measurable operators

Banach envelopes in symmetric spaces of measurable operators We study Banach envelopes for commutative symmetric sequence or function spaces, and noncommutative symmetric spaces of measurable operators. We characterize the class (HC) of quasi-normed symmetric sequence or function spaces E for which their Banach envelopes $$\widehat{E}$$ E ^ are also symmetric spaces. The class of symmetric spaces satisfying (HC) contains but is not limited to order continuous spaces. Let $$\mathcal {M}$$ M be a non-atomic, semifinite von Neumann algebra with a faithful, normal, $$\sigma$$ σ -finite trace $$\tau$$ τ and E be as symmetric function space on $$[0,\tau (\mathbf 1 ))$$ [ 0 , τ ( 1 ) ) or symmetric sequence space. We compute Banach envelope norms on $$E(\mathcal {M},\tau )$$ E ( M , τ ) and $$C_E$$ C E for any quasi-normed symmetric space E. Then we show under assumption that $$E\in (HC)$$ E ∈ ( H C ) that the Banach envelope $$\widehat{E(\mathcal {M},\tau )}$$ E ( M , τ ) ^ of $$E(\mathcal {M},\tau )$$ E ( M , τ ) is equal to $$\widehat{E}\left( \mathcal {M},\tau \right)$$ E ^ M , τ isometrically. We also prove the analogous result for unitary matrix spaces $$C_E$$ C E . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Banach envelopes in symmetric spaces of measurable operators

, Volume 21 (1) – Jun 7, 2016
20 pages

/lp/springer_journal/banach-envelopes-in-symmetric-spaces-of-measurable-operators-ctskF8nDhI
Publisher
Springer International Publishing
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/s11117-016-0430-4
Publisher site
See Article on Publisher Site

DeepDyve is your personal research library

It’s your single place to instantly
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