On unitary equivalence of bilateral operator valued weighted shifts

• Autorzy: Kośmider Jakub

Identyfikatory

DOI

10.7494/OpMath.2019.39.4.543

• Języki publikacji: EN

Abstrakty

EN

We establish a characterization of unitary equivalence of two bilateral operator valued weighted shifts with quasi-invertible weights by an operator of diagonal form. We provide an example of unitary equivalence between shifts with weights defined on C2 which cannot be given by any unitary operator of diagonal form. The paper also contains some remarks regarding unitary operators that can give unitary equivalence of bilateral operator valued weighted shifts.

Słowa kluczowe

EN

unitary equivalence; bilateral weighted shift quasi-invertible weights; partial isometry

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2019
• Tom: Vol. 39, no. 4
• Strony: 543--555
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Kośmider Jakub

• Instytut Matematyki Uniwersytet Jagielloński ul. Łojasiewicza 6, 30-348 Kraków, Poland

Bibliografia

• [1] A. Anand, S. Chavan, Z.J. Jabłoński, J. Stochel, Complete systems of unitary invariants for some classes of 2-isornetries, Banach J. Math. Anal. 13 (2019) 2, 359-385.
• [2] A. Athavale, On completely hyperexpansive operators, Proc. Amer. Math. Soc. 124 (1996), 3745-3752.
• [3] A. Bourhim, C.E. Chidume, The single-valued extension property for bilateral operator weighted shifts, Proc. Amer. Math. Soc, 133 (2004), 485-491.
• [4] J.B. Conway, A Course in Functional Analysis, Springer-Verlag, New York, 1990.
• [5] G.P. Geher, Bilateral weighted shift operators similar to normal operators, Oper. Matrices 10 (2016) 2, 419-423.
• [6] J. Guyker, On reducing subspaces of normally weighted bilateral shifts, Houston J. Math. 11 (1985) 4, 515-521.
• [7] R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge University Press, 1990.
• [8] N. Ivanovski, Simitiarity and quasisimiliarity of bilateral operator valued weighted shifts, Mat. Bilten 17 (1993), 33-37.
• [9] Z.J. Jabłoński, Hyperexpansive operator valued unilateral weighted shifts, Glasg. Math. J. 46 (2004), 405-416.
• [10] Z.J. Jabłoński, IB. Jung, J. Stochel, Weighted Shifts on Directed Trees, Mem. Amer. Math. Soc. 216 (2012) 1017.
• [11] A. Lambert, Unitary equivalence and reducibility of invertibly weighted shifts, Bull. Aust. Math. Soc. 5 (1971), 157-173.
• [12] J.X. Li, Y.Q. Ji, S.L. Sun, The essential spectrum, and Banach reducibility of operator weighted shifts, Acta Math. Sin., English Series, 17 (2001) 3, 413-424.
• [13] M. Orovcanec, Unitary equivalence of unilateral operator valued weighted shifts with quasi-invertible weights, Mat. Bilten 17 (1993), 45-50.
• [14] P. Pietrzycki, The single equality A*nAn = (A* A)n does not imply the quasinormality of weighted shifts on rootless directed trees, J. Math. Anal. Appl. 435 (2016), 338-348.
• [15] V.S. Pilidi, On unitary equivalence of multiple weighted shift operators, Teor. Funkts. Funkts. Anal. Prilozh. 34 (1980), 96-103 [in Russian].
• [16] A. Shields, Weighted shift operators, analytic function theory, Topics in Operator Theory, Math. Surveys 13, Amer. Math. Soc, Providence, R. I. (1974), 49-128.