## A characterization of smooth functions defined on a Banach space

Publication
, Journal Article

Hain, RM

Published in: Proceedings of the American Mathematical Society

1979

A sufficient condition for a function defined on a Banach space to be is given. This enables us to characterize the functions from one Banach space into another Banach space as those functions that, for each positive integer , have the property that the composition of the function with each function from into the domain of the function is .

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## Published In

Proceedings of the American Mathematical Society

## DOI

## EISSN

1088-6826

## ISSN

0002-9939

## Publication Date

1979

## Volume

77

## Issue

1

## Start / End Page

63 / 67

## Publisher

American Mathematical Society (AMS)

## Related Subject Headings

- 4904 Pure mathematics
- 0101 Pure Mathematics

### Citation

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MLA

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Hain, R. M. (1979). A characterization of smooth functions defined on a Banach space.

*Proceedings of the American Mathematical Society*,*77*(1), 63–67. https://doi.org/10.1090/s0002-9939-1979-0539632-8Hain, Richard M. “A characterization of smooth functions defined on a Banach space.”

*Proceedings of the American Mathematical Society*77, no. 1 (1979): 63–67. https://doi.org/10.1090/s0002-9939-1979-0539632-8.Hain RM. A characterization of smooth functions defined on a Banach space. Proceedings of the American Mathematical Society. 1979;77(1):63–7.

Hain, Richard M. “A characterization of smooth functions defined on a Banach space.”

*Proceedings of the American Mathematical Society*, vol. 77, no. 1, American Mathematical Society (AMS), 1979, pp. 63–67.*Crossref*, doi:10.1090/s0002-9939-1979-0539632-8.Hain RM. A characterization of smooth functions defined on a Banach space. Proceedings of the American Mathematical Society. American Mathematical Society (AMS); 1979;77(1):63–67.

## Published In

Proceedings of the American Mathematical Society

## DOI

## EISSN

1088-6826

## ISSN

0002-9939

## Publication Date

1979

## Volume

77

## Issue

1

## Start / End Page

63 / 67

## Publisher

American Mathematical Society (AMS)

## Related Subject Headings

- 4904 Pure mathematics
- 0101 Pure Mathematics