Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Anticommutant lifting and anticommuting dilation

Author: Zoltán Sebestyén
Journal: Proc. Amer. Math. Soc. 121 (1994), 133-136
MSC: Primary 47A20; Secondary 47N70, 93C05
MathSciNet review: 1176485
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we prove the anticommutant counterpart of the Sz.-Nagy-Foiaş commutant lifting theorem and Ando's theorem on unitary dilation of a pair of commutative contractions. A dual extension theorem applies in the one-step procedure of our approach.

References [Enhancements On Off] (What's this?)

  • [1] T. Ando, On a pair of commutative contractions, Acta Sci. Math. (Szeged) 24 (1963), 88-90. MR 0155193 (27:5132)
  • [2] C. Foiaş and A. Tannenbaum, A strong Parrot theorem, Proc. Amer. Math. Soc. 106 (1989), 777-784. MR 972228 (90d:47011)
  • [3] S. Parrott, On the quotient norm and the Sz.-Nagy-Foiaş lifting theorem, J. Funct. Anal. 30 (1978), 311-328. MR 518338 (81h:47006)
  • [4] Z. Sebestyén, A proof of Parrott's theorem on quotient norms, Period Math. Hungar. 20 (1989), 85-87. MR 1001506 (90h:47019)
  • [5] -, Parrott's theorem versus strong Parrott theorem, Semesterberichte Funktionalanalysis Tübingen, Wintersemester 89/90, pp. 227-229.
  • [6] Z. Sebestyén and Á. Magyar, Compact self-adjoint extensions of suboperators, Linear Algebra Appl. (submitted).
  • [7] B. Sz.-Nagy and C. Foiaş, Dilation des commutants d'operateurs, C. R. Acad. Sci. Paris Sér. I Math. 266 (1968), 493-495. MR 0236755 (38:5049)
  • [8] -, Harmonic analysis of operators on Hilbert space, North-Holland, Amsterdam, 1970.
  • [9] R. G. Douglas, P. S. Muhly, and C. Pearcy, Lifting commuting operators, Michigan Math. J. 15 (1968), 385-395. MR 0236752 (38:5046)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A20, 47N70, 93C05

Retrieve articles in all journals with MSC: 47A20, 47N70, 93C05

Additional Information

Keywords: Sz.-Nagy-Foiaş commutant lifting, Parrott's theorem, Ando's theorem, dilation theory, one-step extension, anticommuting contractions and unitaries
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society