Proceedings of the Centre for Mathematics and its Applications

Non isomorphism of the disc algebra with spaces of differentiable functions

A. Pełczyński

Full-text: Open access

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

Source
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

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


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