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1996 | 119 | 1 | 65-76
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Decomposable embeddings, complete trajectories, and invariant subspaces

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We produce closed nontrivial invariant subspaces for closed (possibly unbounded) linear operators, A, on a Banach space, that may be embedded between decomposable operators on spaces with weaker and stronger topologies. We show that this can be done under many conditions on orbits, including when both A and A* have nontrivial non-quasi-analytic complete trajectories, and when both A and A* generate bounded semigroups that are not stable.
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Bibliografia
  • [A] A. Atzmon, On the existence of hyperinvariant subspaces, J. Operator Theory 11 (1984), 3-40.
  • [B] B. Beauzamy, Sous-espaces invariants de type fonctionnel, Acta Math. 144 (1980), 65-82.
  • [vC] J. A. van Casteren, Generators of Strongly Continuous Semigroups, Res. Notes Math. 115, Pitman, Boston, 1985.
  • [Co-F] I. Colojoăra and C. Foiaş, Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968.
  • [Da] E. B. Davies, One-Parameter Semigroups, London Math. Soc. Monographs 15, Academic Press, 1980.
  • [dL] R. deLaubenfels, Existence Families, Functional Calculi and Evolution Equations, Lecture Notes in Math. 1570, Springer, 1994.
  • [dL-Ka] R. deLaubenfels and S. Kantorovitz, Laplace and Laplace-Stieltjes spaces, J. Funct. Anal. 116 (1993), 1-61.
  • [Du-S] N. Dunford and J. T. Schwartz, Linear Operators, Part III, Interscience, New York, 1971.
  • [E-W] I. Erdelyi and S. Wang, A Local Spectral Theory for Closed Operators, London Math. Soc. Lecture Note Ser. 105, Cambridge Univ. Press, 1985.
  • [G] J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford Univ. Press, New York, 1985.
  • [H] S. Huang, Characterizing spectra of closed operators through existence of slowly growing solutions of their Cauchy problems, Studia Math. 116 (1995), 23-41.
  • [Ka] S. Kantorovitz, The Hille-Yosida space of an arbitrary operator, J. Math. Anal. Appl. 136 (1988), 107-111.
  • [Kr-Lap-Cv] S. G. Krein, G. I. Laptev and G. A. Cvetkova, On Hadamard correctness of the Cauchy problem for the equation of evolution, Soviet Math. Dokl. 11 (1970), 763-766.
  • [Lan-W] R. Lange and S. Wang, New Approaches in Spectral Decomposition, Contemp. Math. 128, Amer. Math. Soc., Providence, 1992.
  • [Lau-Ne] K. B. Laursen and M. M. Neumann, Asymptotic intertwining and spectral inclusions on Banach spaces, Czechoslovak Math. J. 43 (1993), 483-497.
  • [Lyu-Mat] Yu. I. Lyubich and V. I. Matsaev, On operators with separable spectrum, Math. USSR-Sb. 56 (1962), 433-468.
  • [Mar] E. Marschall, On the functional calculus of non-quasianalytic groups of operators and cosine functions, Rend. Circ. Mat. Palermo 35 (1986), 58-81.
  • [Na] R. Nagel (ed.), One-Parameter Semigroups of Positive Operators, Lecture Notes in Math. 1184, Springer, 1986.
  • [Ne] M. M. Neumann, Local spectral theory for operators on Banach spaces and applications to convolution operators on group algebras, in: Louisiana State Univ. Seminar Notes in Funct. Anal. and PDEs, 1993-94, 287-308.
  • [P] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
  • [Va] F. H. Vasilescu, Analytic Functional Calculus and Spectral Decompositions, D. Reidel, Bucharest-Dordrecht, 1982.
  • [Vũ1] Vũ Quôc Phóng, On the spectrum, complete trajectories, and asymptotic stability of linear semi-dynamical systems, J. Differential Equations 105 (1993), 30-45.
  • [Vũ2] Vũ Quôc Phóng, Semigroups with nonquasianalytic growth, Studia Math. 104 (1993), 229-241.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv119i1p65bwm
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