Change search
ReferencesLink to record
Permanent link

Direct link
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, 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
URN: urn:nbn:se:kth:diva-93916DOI: 10.1007/s11785-011-0165-yISI: 000301976500009ScopusID: 2-s2.0-84858792109OAI: diva2:525142
QC 20120507Available from: 2012-05-07 Created: 2012-05-03 Last updated: 2012-05-07Bibliographically 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

Search outside of DiVA

GoogleGoogle Scholar
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

Altmetric score

Total: 29 hits
ReferencesLink to record
Permanent link

Direct link