## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- Miniconference on Probability and Analysis. Ian Doust and Brian Jefferies, eds. Proceedings of the Centre for Mathematics and its Applications, v. 29. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1992), 183 - 195

### Non isomorphism of the disc algebra with spaces of differentiable functions

#### Abstract

It is proved that the Disc Algebra does not contain a complemented subspace isomorphic to the space $C_{(k)}(T^d) of $k$ times continuously differentiable functions on the $d$-dimensional torus $(k = 1,2,...; d = 2,3,...)$.

#### Article information

**Dates**

First available in Project Euclid:
18 November 2014

**Permanent link to this document**

https://projecteuclid.org/
euclid.pcma/1416322702

**Mathematical Reviews number (MathSciNet)**

MR1188895

**Zentralblatt MATH identifier**

0796.46013

#### Citation

Pełczyński, A. Non isomorphism of the disc algebra with spaces of differentiable functions. Miniconference on Probability and Analysis, 183--195, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1992. https://projecteuclid.org/euclid.pcma/1416322702