Unitary extensions of two-parameter local semigroups of isometric operators and the Krein extension theorem |
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| Authors: | Ramón Bruzual |
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| Affiliation: | (1) Dpto. de Matematica. Facultad de Ciencias, Universidad Central de Venezuela, Venezuela;(2) Present address: Los Chaguaramos, Apartado 47686, 1041-A Caracas, Venezuela |
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| Abstract: | A notion of two-parameter local semigroups of isometric operators in Hilbert space is discussed. It is shown that under certain conditions such a semigroup can be extended to a strongly continuous two-parameter group of unitary operators in a larger Hilbert space. As an application a simple proof of the Eskin bidimensional version of the Krein extension theorem is given. |
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| Keywords: | Primary 47D03 Secondary 42A82 |
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