Non isomorphism of the disc algebra with spaces of differentiable functions. (English) Zbl 0796.46013

Pełczyński, A.

Doust, Ian (ed.) et al., Proceedings of the miniconference on probability and analysis, held at the University of New South Wales, Sydney, Australia, July 24-26, 1991. Canberra: Centre for Mathematics and Its Applications, Australian National University. Proc. Cent. Math. Appl. Aust. Natl. Univ. 29, 183-195 (1991).

Summary: It is proved that the disc algebra does not contain a complemented subspace isomorphic to the space \(C_{(k)}(\mathbb{T}^ d)\) of \(k\) times continuously differentiable functions on the \(d\)-dimensional torus \((k=1,2,\dots\); \(d=2,3,\dots)\).
For the entire collection see [Zbl 0782.00061].

MSC:

46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46B20	Geometry and structure of normed linear spaces
46J15	Banach algebras of differentiable or analytic functions, \(H^p\)-spaces

Keywords:

disc algebra; complemented subspace