Control on weak asymptotic abelianness with the help of the crossed product construction

Heide Narnhofer

Banach Center Publications (1998)

  • Volume: 43, Issue: 1, page 331-339
  • ISSN: 0137-6934

Abstract

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The crossed product construction is used to control in some examples the asymptotic behaviour of time evolution. How invariant states on a small algebra can be extended to invariant states on a larger algebra reduces to solving an eigenvalue problem. In some cases (the irrational rotation algebra) this eigenvalue problem has only trivial solutions and by reduction of the subalgebra control on all invariant states can be found.

How to cite

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Narnhofer, Heide. "Control on weak asymptotic abelianness with the help of the crossed product construction." Banach Center Publications 43.1 (1998): 331-339. <http://eudml.org/doc/208854>.

@article{Narnhofer1998,
abstract = {The crossed product construction is used to control in some examples the asymptotic behaviour of time evolution. How invariant states on a small algebra can be extended to invariant states on a larger algebra reduces to solving an eigenvalue problem. In some cases (the irrational rotation algebra) this eigenvalue problem has only trivial solutions and by reduction of the subalgebra control on all invariant states can be found.},
author = {Narnhofer, Heide},
journal = {Banach Center Publications},
keywords = {asymptotic abelianness; crossed product construction; asymptotic behaviour of time evolution; invariant states; eigenvalue problem; irrational rotation algebra},
language = {eng},
number = {1},
pages = {331-339},
title = {Control on weak asymptotic abelianness with the help of the crossed product construction},
url = {http://eudml.org/doc/208854},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Narnhofer, Heide
TI - Control on weak asymptotic abelianness with the help of the crossed product construction
JO - Banach Center Publications
PY - 1998
VL - 43
IS - 1
SP - 331
EP - 339
AB - The crossed product construction is used to control in some examples the asymptotic behaviour of time evolution. How invariant states on a small algebra can be extended to invariant states on a larger algebra reduces to solving an eigenvalue problem. In some cases (the irrational rotation algebra) this eigenvalue problem has only trivial solutions and by reduction of the subalgebra control on all invariant states can be found.
LA - eng
KW - asymptotic abelianness; crossed product construction; asymptotic behaviour of time evolution; invariant states; eigenvalue problem; irrational rotation algebra
UR - http://eudml.org/doc/208854
ER -

References

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  9. [9] D.C. Mattis and E. Lieb, J. Math. Phys. 6 (1965) 304. 
  10. [0] H. Narnhofer and W. Thirring, Phys. Rev. A 26/6 (1982) 3646. 
  11. [11] H. Narnhofer and W. Thirring, Spontaneously Broken Symmetry, Vienna preprint (1997). 
  12. [12] H. Narnhofer, Properties of Automorphisms on the Rotation Algebra, Vienna preprint (1997). Zbl0914.46057
  13. [13] F. Riesz and B. Sz-Nagy, Leçons d'analyse fonctionnelle, 6. ed. Gauthier-Villars, Paris, 1972. 
  14. [14] D. Ruelle, Statistical Mechanics, Benjamin, New York, 1969. 

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