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
Cauchy Integrals Method in the Study of Perturbations of Operators
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2016 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Metoden av Cauchyintegraler i studien av perturbationer av operatorer (Swedish)
Abstract [en]

We show that functions which are analytic on the open unit disc and fulfil the Hölder condition of order r  there, where r lies in the interval (0,1), are operator Hölder of order r on the set of all linear contractions on a Hilbert space. Further, it is known that analytic Lipschitz functions on the unit disc need not be operator Lipschitz. We show that under a certain additional integral condition, these functions are operator Lipschitz. The two results are shown by tools from operator theory including the Spectral theorem and dilations of contractions.

We also solve a problem related to theory of dilations which was arisen on a mathematical question- and answer site. More specificaly we show that, for a certain operator-valued polynomial, the von Neumann inequality is false.

Abstract [sv]

Vi visar att analytiska funktioner på öppna enhetsskivan som uppfyller Höldervillkoret av ordning r, där r ligger på intervallet (0,1), är operator Hölder av ordning r på mängden av alla linjära kontraktioner på ett Hilbert rum. Vidare så är det känt att analytiska Lipschitzfunktioner på enhetsskivan inte behöver vara operator-Lipschitz. Vi visar att om vi lägger till ett visst integralvillkor så är dessa funktioner operator-Lipschitz. Vi visar de två resultaten med redskap från operatorteori som inkluderar Spektralsatsen och dilationer av kontraktioner.

Vi löser även ett problem som är relaterat till teorin om dilationer som uppstod på en matematisk frågor- och svarhemsida. Mer specifikt visar vi att för ett visst polynom som antar operatorvärden så är von Neumanns olikhet falsk.

Place, publisher, year, edition, pages
2016.
Series
TRITA-MAT-E, 2016:15
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-187351OAI: oai:DiVA.org:kth-187351DiVA: diva2:933300
Subject / course
Mathematics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2016-06-03 Created: 2016-05-20 Last updated: 2016-06-03Bibliographically approved

Open Access in DiVA

fulltext(636 kB)59 downloads
File information
File name FULLTEXT01.pdfFile size 636 kBChecksum SHA-512
5a516206809fc650b29f6606e958b51328268ab68bdc4a68fcbef66a8f76088c6f03027e018ce0f320259a593b20fd44aa9572e400f8cef19a0a4fb3260253b3
Type fulltextMimetype application/pdf

By organisation
Mathematics (Div.)
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 59 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: 130 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