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Contraction Groups and Equivalent Norms*

Published online by Cambridge University Press:  22 January 2016

William G. Vogt ,
Martin M. Eisen  and
Gabe R. Buis
William G. Vogt
Affiliation:
University of Pittsburgh, Pittsburgh, Pa., U.S.A.
Martin M. Eisen
Affiliation:
University of Pittsburgh, Pittsburgh, Pa., U.S.A.
Gabe R. Buis
Affiliation:
University of Pittsburgh, Pittsburgh, Pa., U.S.A.
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Using the notation in [1], the Lumer-Phillips theorem (3. 1 of [2]) is refined to single parameter groups in real Banach space and real Hilbert space. The theory can be extended to complex spaces.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 34 , March 1969 , pp. 149 - 151
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1969

Footnotes

†

Presently with TRW Systems Group, Redondo Beach, California, U.S.A.

*

This research was supported in part by the National Aeronautics and Space Administration under Grant No. NGR 39-011-039 with the University of Pittsburgh

References

[1] Yosida, K., Functional Analysis, Springer-Verlag, Berlin (1965).Google Scholar
[2] Lumer, G. and Phillips, R.S., “Dissipative operators in a Banach space,” Pacific J. Math, 11, (1961) 679–698.CrossRefGoogle Scholar
[3] Feller, W., “On the generation of unbounded semi-groups of bounded Linear Operators,” Ann. of Math, 58, (1953) 166–174.Google Scholar