WEIGHTED SHIFTS ON DIRECTED TREES WITH ONE BRANCHING VERTEX : n-CONTRACTIVITY AND HYPONORMALITY

[1] G. Adams and G. Exner: k-hyponormality and n-contractivity for Agler-type shifts, J. Operator Theory 71 (2014), 585–600.

[2] J. Agler: Hypercontractions and subnormality, J. Operator Theory 13 (1985), 203–217.

[3] P. Budzynski, Z. Jabło ´ nski, I.B. Jung and J. Stochel: ´ A subnormal weighted shift on a directed tree whose n-th power has trivial domain, J. Math. Anal. Appl. 435 (2016), 302–314.

[4] R. Curto: Joint hyponormality: A bridge between hyponormality and subnormality; in Operator theory: operator algebras and applications, Part 2 (Durham, NH, 1988), Proc. Sympos. Pure Math. 51 (1990), Part II, Amer. Math. Soc., Providence, RI, 1990, 69–91.

[5] G. Exner: On n-contractive and n-hypercontractive operators, Integral Equations Operator Theory 56 (2006), 451–468.

[6] G. Exner: Mixed Bram-Halmos and Agler-Embry conditions, J. Math. Anal. Appl. 451 (2017), 544–564.

[7] G. Exner, I.B. Jung and S. Park: On n-contractive and n-hypercontractive operators, II, Integral Equations Operator Theory 60 (2008), 451–467.

[8] G. Exner, I.B. Jung, J. Stochel and S.H. Yun: A subnormal completion problem for weighted shifts on directed trees, Integral Equations Operator Theory 90 (2018), Paper No. 72, 36pp.

[9] C. Gu: On (m, p)-expansive and (m, p)-contractive operators on Hilbert and Banach spaces, J. Math. Anal. Appl. 426 (2015), 893–916.

[10] C. Gu and Z. Chen: A model for (n, p)-hypercontractions on Banach space, Indag. Math. 26 (2015), 485– 494.

[11] Z.J. Jabłonski, I.B. Jung and J. Stochel: Weighted shifts on directed trees, Mem. Amer. Math. Soc. ´ 216 (2012), no. 1017.

[12] Z.J. Jabłonski, I.B. Jung and J. Stochel: ´ A hyponormal weighted shift on a directed tree whose square has trivial domain, Proc. Amer. Math. Soc. 142 (2014), 3109–3116.

[13] Z.J. Jabłonski, I.B. Jung and J. Stochel: ´ A non-hyponormal operator generating Stieltjes moment sequences, J. Funct. Anal. 262 (2012), 3946–3980