한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제18권1호
  • /
  • Pages.31-39
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  • 2011
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  • 1226-0657(pISSN)
  • /
  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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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)
  • 투고 : 2010.07.19
  • 심사 : 2010.12.24
  • 발행 : 2011.02.28
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초록

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.

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참고문헌

  1. E.C. Lance: Hilbert $C^{\ast}-Modules$. LMS Lecture Note Series 210, Cambridge University Press, 1995.
  2. G.J. Murphy: $C^{\ast}-Algebras$ and Operator Theory. Academic press, New York, 1990.
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  5. M.H. Stone: On one-parameter unitary groups in Hilbert space. Ann. Math. 33 (1932), no. 3, 643-648. https://doi.org/10.2307/1968538
  6. K. Yosida: Functional Analysis. Springer-Verlag, 1968.
  7. L.C. Zhang & M.Z. Guo: A Stone-type theorem (Chinese). Acta Math. Sinica (Chin. Ser.) 50 (2007), no. 4, 857-860.