Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • 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
Projective Freeness of Algebras of Real Symmetric Functions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2012 (English)In: Complex Analysis and Operator Theory, ISSN 1661-8254, E-ISSN 1661-8262, Vol. 6, no 2, 465-475 p.Article in journal (Refereed) Published
Abstract [en]

Let D-n := {z = (z(1),...,z(n)) is an element of C-n : vertical bar z(j)vertical bar < 1, j = 1,...,n}, and let <(D)over bar>(n) denote its closure in C-n. Consider the ring C-r((D) over bar (n); C) = {f : (D) over bar (n) -> C : f is continuous and f (z) = <(f<(z)over bar>)over bar> (z is an element of (D) over bar (n))} with pointwise operations, where u is used appropriately to denote both (componentwise) complex conjugation and closure. It is shown that C-r((D) over bar (n); C) is projective free, that is, finitely generated projective modules over C-r((D) over bar (n); C) are free. Let A denote the polydisc algebra, that is, the set of all continuous functions defined on (D) over bar (n) that are holomorphic in D-n. For N a positive integer, let partial derivative(-N) A denote the algebra of functions f is an element of A whose complex partial derivatives of all orders up to N belong to A. We show the projective freeness of each of the real symmetric algebras partial derivative(-N) A(r) = {f is an element of partial derivative(-N) A : f (z) = <(f<(z)over bar>)over bar> (z is an element of (D) over bar (n))}.

Place, publisher, year, edition, pages
2012. Vol. 6, no 2, 465-475 p.
Keyword [en]
Real Banach algebras, Projective free rings, Serre's conjecture, Real symmetric function algebras, Control theory
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-93916DOI: 10.1007/s11785-011-0165-yISI: 000301976500009Scopus ID: 2-s2.0-84858792109OAI: oai:DiVA.org:kth-93916DiVA: diva2:525142
Note
QC 20120507Available from: 2012-05-07 Created: 2012-05-03 Last updated: 2017-12-07Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Sasane, Amol
By organisation
Mathematics (Dept.)
In the same journal
Complex Analysis and Operator Theory
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

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

Direct link
Cite
Citation style
  • apa
  • harvard1
  • 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