Kreĭn space unitary dilations of Hilbert space holomorphic semigroups

• Autores: Stefania Marcantognini
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 61, Nº. 1, 2020, págs. 145-160
• Idioma: inglés
• DOI: 10.33044/revuma.v61n1a09
• Enlaces
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• Resumen

  • The infinitesimal generator A of a strongly continuous semigroup on a Hilbert space is assumed to satisfy that Bβ := A−β is a sectorial operator of angle less than π 2 for some β ≥ 0. If Bβ is dissipative in some equivalent scalar product then the Naimark–Arocena representation theorem is applied to obtain a Krein space unitary dilation of the semigroup.

• Referencias bibliográficas
  • T. Ando, Linear operators on Kre˘ın spaces, Hokkaido University, Research Institute of Applied Electricity, Division of Applied Mathematics,...
  • R. Arocena, Scattering functions, Fourier transforms of measures, realization of linear systems and dilations of operators to Kre˘ın spaces:...
  • T. Ya. Azizov and I. S. Iokhvidov, Linear operators in spaces with an indefinite metric, Wiley, Chichester, 1989. MR 1033489.
  • J. Bognár, Indefinite inner product spaces, Springer-Verlag, New York, 1974. MR 0467261.
  • C. Davis, Dilation of uniformly continuous semi-groups, Rev. Roumaine Math. Pures Appl. 15 (1970), 975–983. MR 0268718.
  • M. A. Dritschel and J. Rovnyak, Extension theorems for contraction operators on Kre˘ın spaces, in Extension and interpolation of linear operators...
  • M. A. Dritschel and J. Rovnyak, Operators on indefinite inner product spaces, in Lectures on operator theory and its applications (Waterloo,...
  • M. Haase, The functional calculus for sectorial operators, Operator Theory: Advances and Applications, 169, Birkhäuser Verlag, Basel, 2006....
  • T. Kato, Perturbation theory for linear operators, Springer-Verlag, Berlin, 1980.
  • B. McEnnis, Dilations of holomorphic semigroups, J. Operator Theory 23 (1990), no. 1, 21–42. MR 1054813.
  • A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, 44, Springer-Verlag,...
  • K. Yosida, Functional analysis, fourth edition, Springer-Verlag, New York, 1974. MR 0350358.