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On Generalized Morse-Transue Function Spaces

Published online by Cambridge University Press:  20 November 2018

H. W. Ellis
H. W. Ellis*
Affiliation:
Queen's University, Summer Research Institute of the Canadian Mathematical Congress
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Marston Morse and William Transue (6, 8) have introduced and studied function spaces, called MT-spaces, for which the elements of the topological dual are of integral type. Their theory does not admit certain classical Banach function spaces including spaces of bounded functions and spaces. The theory of function spaces determined by a length function (λ-spaces) (4, 5), which depends on a fixed measure, admits many of the maximal MT-spaces, the spaces and spaces of locally integrable functions but does not admit certain maximal MT-spaces including the space of complex continuous functions with compact supports.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 416 - 426
Copyright
Copyright © Canadian Mathematical Society 1959

References

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