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http://dx.doi.org/10.7468/jksmeb.2011.18.1.031

A GENERALIZATION OF STONE'S THEOREM IN HILBERT $C^*$ -MODULES

Amyari, Maryam (Department of Mathematics, Faculty of science, Islamic Azad University-Mashhad Branch)
Chakoshi, Mahnaz (Department of Mathematics, Faculty of science, Islamic Azad University-Mashhad Branch)

Publication Information

The Pure and Applied Mathematics / v.18, no.1, 2011 , pp. 31-39 More about this Journal

Abstract

Stone's theorem states that "A bounded linear operator A is infinitesimal generator of a $C_0$ -group of unitary operators on a Hilbert space H if and only if iA is self adjoint". In this paper we establish a generalization of Stone's theorem in the framework of Hilbert $C^*$ -modules.

Keywords

$C_0$ -semigroup; infinitesimal generator; $C_0$ -group; Hilbert $C^*$ -module; unitary operator; adjointable operator;

Citations & Related Records

Reference

1	M.H. Stone: On one-parameter unitary groups in Hilbert space. Ann. Math. 33 (1932), no. 3, 643-648. DOI ScienceOn
2	K. Yosida: Functional Analysis. Springer-Verlag, 1968.
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5	E.C. Lance: Hilbert $C^{\ast}-Modules$ . LMS Lecture Note Series 210, Cambridge University Press, 1995.
6	G.J. Murphy: $C^{\ast}-Algebras$ and Operator Theory. Academic press, New York, 1990.
7	A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York, 1983.

KSCI

A GENERALIZATION OF STONE'S THEOREM IN HILBERT -MODULES

A GENERALIZATION OF STONE'S THEOREM IN HILBERT $C^*$ -MODULES