Rocky Mountain Journal of Mathematics

A Theorem of Krein Revisited

Timur Oikhberg and Vladimir G. Troitsky

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Rocky Mountain J. Math., Volume 35, Number 1 (2005), 195-210.

First available in Project Euclid: 5 June 2007

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Zentralblatt MATH identifier

Primary: 46B40: Ordered normed spaces [See also 46A40, 46B42] 47B60: Operators on ordered spaces 47B65: Positive operators and order-bounded operators
Secondary: 47A15: Invariant subspaces [See also 47A46] 47B48: Operators on Banach algebras 46L05: General theory of $C^*$-algebras 46L10: General theory of von Neumann algebras

Krein theorem ordered normed space cone with interior point positive eigenvector invariant cone invariant subspace invariant ideal invariant set adjoint operator $C^*$-algebra von Neumann algebra


Oikhberg, Timur; Troitsky, Vladimir G. A Theorem of Krein Revisited. Rocky Mountain J. Math. 35 (2005), no. 1, 195--210. doi:10.1216/rmjm/1181069776.

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  • Y.A. Abramovich and C.D. Aliprantis, An invitation to operator theory, Grad. Studies in Math., Amer. Math. Soc., Providence, RI, 2002.
  • Y.A. Abramovich, C.D. Aliprantis and O. Burkinshaw, The invariant subspace problem: Some recent advances, Rend. Istit. Mat. Univ. Trieste 29 Suppl. (1998), 3-79.
  • --------, Positive operators on Kreĭ n spaces, Acta Appl. Math. 27 (1992), 1-22.
  • C.D. Aliprantis and O. Burkinshaw, Positive operators, Academic Press Inc., Orlando, Florida, 1985.
  • P. Dodds, T. Dodds and B. dePagter, Noncommutative Banach function spaces, Math. Z. 201, (1989), 583-597.
  • --------, Noncommutative Köthe duality, Trans. Amer. Math. Soc. 339 (1993), 717-750.
  • N. Dunford and J.T. Schwartz, Linear operators I, Interscience Publishers, Inc., New York, 1958.
  • T. Fack and H. Kosaki, Generalized $s$-numbers of $\tau$-measurable operators, Pacific J. Math. 123 (1986), 269-300.
  • M.G. Kreĭn and M.A. Rutman, Linear operators leaving invariant a cone in a Banach space, Uspehi Matem. Nauk (N.S.) 3 (1948), 3-95 (Russian); Amer. Math. Soc. Transl., 1950(26):128, 1950 (English).
  • Y. Lindenstrauss and L. Tzafriri, Classical Banach spaces II, Springer-Verlag, Berlin, 1979.
  • E. Nelson, Notes on non-commutative integration, J. Funct. Anal. 15 (1974), 103-116.
  • H.H. Schaefer and M.P. Wolff, Topological vector spaces, Springer-Verlag, New York, 1999.
  • M. Takesaki, Theory of operator algebras I, Springer-Verlag, New York, 1979.