PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1997 | 66 | 1 | 105-121
Tytuł artykułu

On the intertwinings of regular dilations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to find conditions that assure the existence of the commutant lifting theorem for commuting pairs of contractions (briefly, bicontractions) having (*-)regular dilations. It is known that in such generality, a commutant lifting theorem fails to be true. A positive answer is given for contractive intertwinings which doubly intertwine one of the components. We also show that it is possible to drop the doubly intertwining property for one of the components in some special cases, for instance for semi-subnormal bicontractions. As an application, a result regarding the existence of a unitary (isometric) dilation for three commuting contractions is obtained.
Rocznik
Tom
66
Numer
1
Strony
105-121
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-07-12
poprawiono
1996-01-08
Twórcy
  • Department of Mathematics, University of Timişoara, Bv. V. Pârvan 4, 1900 Timişoara, Romania
  • Department of Mathematics, University of Timişoara, Bv. V. Pârvan 4, 1900 Timişoara, Romania
Bibliografia
  • [1] T. Ando, On a pair of commutative contractions, Acta Sci. Math. 24 (1963), 88-90.
  • [2] A. Athavale, On the intertwining of joint isometries, J. Operator Theory 23 (2) (1990), 339-350.
  • [3] S. Brehmer, Über vertauschbare Kontraktionen des Hilbertschen Raumes, Acta Sci. Math. (Szeged) 22 (1961), 106-111.
  • [4] R. E. Curto and F. H. Vasilescu, Standard operator models in the polydisc, Indiana Univ. Math. J. 42 (1993), 791-810.
  • [5] C. Foiaş and A. E. Frazho, The Commutant Lifting Approach to Interpolation Problems, Birkhäuser, Basel, 1990.
  • [6] T. Furuta, An extension of the Fuglede-Putnam theorem to subnormal operators using a Hilbert-Schmidt norm inequality, Proc. Amer. Math. Soc. 81 (2) (1981), 240-242.
  • [7] D. Gaşpar and N. Suciu, Intertwining properties of isometric semigroups and Wold-type decompositions, in: Oper. Theory Adv. Appl. 24, Birkhäuser, Basel, 1987, 183-193.
  • [8] D. Gaşpar and N. Suciu, On the Geometric Structure of Regular Dilations, Oper. Theory Adv. Appl., Birkhäuser, 1996.
  • [9] D. Gaşpar and N. Suciu, On intertwining liftings of the distinguished dilations of bicontractions, to appear.
  • [10] I. Halperin, Sz.-Nagy-Brehmer dilations, Acta Sci. Math. (Szeged) 23 (1962), 279-289.
  • [11] M. Kosiek, A. Octavio and M. Ptak, On the reflexivity of pairs of contractions, Proc. Amer. Math. Soc. 123 (1995), 1229-1236.
  • [12] W. Mlak, Intertwining operators, Studia Math. 43 (1972), 219-233.
  • [13] W. Mlak, Commutants of subnormal operators, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 19 (9) (1971), 837-842.
  • [14] V. Müller, Commutant lifting theorem for n-tuples of contractions, Acta Sci. Math. (Szeged) 59 (1994), 465-474.
  • [15] S. Parrott, Unitary dilations for commuting contractions, Pacific J. Math. 34 (1970), 481-490.
  • [16] M. Słociński, Isometric dilations of doubly commuting contractions and related models, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (12) (1977), 1233-1242.
  • [17] M. Słociński, On the Wold-type decomposition of a pair of commuting isometries, Ann. Polon. Math. 37 (1980), 255-262.
  • [18] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam-Budapest, 1970.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv66z1p105bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.