Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Real and complex operator norms between quasi-banach Lp -L q spaces
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0002-9584-4083
Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
2011 (English)In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 14, no 2, 247-270 p.Article in journal (Refereed) Published
Abstract [en]

Relations between the norms of an operator and its complexification as a mapping from Lp to Lq has been recognized as a serious problem in analysis after the publication of Marcel Riesz's work on convexity and bilinear forms in 1926. We summarize here what it is known about these relations in the case of normed Legesgue spaces and investigate the quasinormed case, i. e. we consider all 0 < p,q ≤ 8 . In particular, in the lower triangle, that is, for 0< p≤q≤∞ these norms are the same. In the upper triangle and the normed case, that is, when 1 ≤ q < p ≤ ∞ the norm of the complexification of a real operator is obviously not bigger than 2 times its real norm. In 1977 Krivine proved that the constant 2 can be replaced by √2 . On the other hand, it was suspected that in the case of quasi-normed Lebesgue spaces (0 < q < p ≤ ∞ ) the corresponding constant could be arbitrarily large, but as we will see this is not the case. More precisely, we prove that this constant for quasi-normed Lebesgue spaces is between 1 and 2. Some additional properties and estimates of this constant with some results about the relation between complex and real norms of operators, including those between two-dimensional Orlicz spaces are presented in the first four chapters. Finally, in Chapter 5, we use the results on the estimates of the norms in the proof of the real Riesz-Thorin interpolation theorem valid in the first quadrant

Place, publisher, year, edition, pages
2011. Vol. 14, no 2, 247-270 p.
National Category
Mathematical Analysis Infrastructure Engineering
Research subject
Mathematics; Structural Engineering
Identifiers
URN: urn:nbn:se:ltu:diva-7220Local ID: 58d4be7b-a1da-4013-99b2-14297028fe87OAI: oai:DiVA.org:ltu-7220DiVA: diva2:980109
Note
Validerad; 2011; 20110317 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

Open Access in DiVA

fulltext(282 kB)52 downloads
File information
File name FULLTEXT01.pdfFile size 282 kBChecksum SHA-512
46ede25be8c134ce0de0d9002539786ed20f973d40b77c3146fc8a222507ad1d12aff301fb39faf644df74b86027c8d998563c955d028d3f1ed08c1d7a00d787
Type fulltextMimetype application/pdf

Other links

http://mia.ele-math.com/14-21/Real-and-complex-operator-norms-between-quasi-Banach-Lp-Lq-spaces

Search in DiVA

By author/editor
Maligranda, LechSabourova, Natalia
By organisation
Mathematical ScienceStructural and Construction Engineering
In the same journal
Mathematical Inequalities & Applications
Mathematical AnalysisInfrastructure Engineering

Search outside of DiVA

GoogleGoogle Scholar
Total: 52 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 38 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf