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

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