Tensor products and joint spectra for solvable Lie algebras of operators

• Autores: Enrico Boasso
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 49, Fasc. 1, 1998, págs. 9-16
• Idioma: inglés
• Enlaces
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• Resumen

  • Given two complex Hilbert spaces, $H_1$ and $H_2$, and two complex solvable finite dimensional Lie algebras of operators, $L_1$ and $L_2$, such that $L_i$ acts on $H_i$ (i= 1,2), the joint spectrum of the Lie algebra $L_1\times\ L_2$, which acts on $H_1\overline{\otimes}H_2$, is expressed by the cartesian product of $Sp(L_1,H_1)$ and $Sp(L_2,H_2)$.

• Referencias bibliográficas
  • E. Boasso and A. Larotonda, A spectral theory for solvable Lie algebras of operators, Pacific J. Math. 158(1) (1993), 15–22.
  • Z. Ceaușescu and F.H. Vasilescu, Tensor products and Taylor’s joint spectrum, Studia Math. 62 (1978), 305–311.
  • Z. Ceaușescu and F.H. Vasilescu, Tensor products and the joint spectrum in Hilbert spaces, Proc. Amer. Math. Soc. 72(3) (1978), 505–508.
  • P. Halmos, Introduction to Hilbert spaces and the theory of spectral multiplicity, Chelsea Publishing Company, 1972.
  • C. Ott, A note on a paper of E. Boasso and A. Larotonda, Pacific J. Math. 173(1) (1996), 173–179.
  • J.L. Taylor, A joint spectrum for several commuting operators, J. Funct. Anal. 6 (1970), 172–191.
  • F.H. Vasilescu, Analytical perturbations of the $\delta$-operator and integral representation formulas in Hilbert spaces, J. Operator Theory...
  • C. Grosu and F.H. Vasilescu, The Künneth formula for Hilbert complexes, Integral Equations Operator Theory 5 (1982), 1–17.