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Invariant Subspaces of Continuous Functions

Published online by Cambridge University Press:  20 November 2018

Morisuke Hasumi  and
T. P. Srinivasan
Morisuke Hasumi
Affiliation:
University of California, Berkeley, and Pan jab University, Chandigarh, India
T. P. Srinivasan
Affiliation:
University of California, Berkeley, and Pan jab University, Chandigarh, India
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Since Beurling (1 ), the study of closed invariant subspaces of Hp(X) and Lp(X) on the unit circle X = {z:|z| = 1} has been done extensively and culminated into a very fine theory of generalized analytic functions ; cf. Hoffman (4), Srinivasan (7). Here we say that a space E of complex-valued functions on X is invariant if zE ⊆ E. Little is known, however, about the structure of closed invariant subspaces E of the space C(X) of continouus functions on X.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 643 - 651
Copyright
Copyright © Canadian Mathematical Society 1965

References

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