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Research Article

Asymptotic properties for compressions of two-isometries

Pages 2177-2202 | Received 14 Feb 2022, Published online: 07 Oct 2022

References

  • J. Agler, An abstract approach to model theory, in Surveys of Some Recent Results in Operator Theory, Vol. II, Pitman Res. Notes Math. Ser., Vol. 192, pp. 1–23, John Wiley and Sons, New York, 1988.
  • J. Agler and M. Stankus, m-isometric transformations of Hilbert spaces, Integral Equations Operator Theory 21(4) (1995), 383–429. doi: 10.1007/BF01222016
  • J. Agler and M. Stankus, m-isometric transformations of Hilbert spaces II, Integral Equations Operator Theory 23(1) (1995), 1–48. doi: 10.1007/BF01261201
  • J. Agler and M. Stankus, m-isometric transformations of Hilbert spaces III, Integral Equations Operator Theory 24(4) (1996), 379–421. doi: 10.1007/BF01191619
  • A. Aleman, The multiplication operator on Hilbert spaces of analytic functions, Habilitationsschrift, Fern Universität, Hagen, 1993.
  • A. Anand, S. Chavan, Z.J. Jabłoński, and J. Stochel, A solution to the Cauchy dual subnormality problem for 2-isometries, J. Funct. Anal. 277(12) (2019), 108292. doi: 10.1016/j.jfa.2019.108292
  • C. Badea, V. Müller, and L. Suciu, High order isometric liftings and dilations, Studia Math. 258(1) (2021), 87–101. doi: 10.4064/sm200330-25-8
  • C. Badea and L. Suciu, The Cauchy dual and 2-isometric liftings of concave operators, J. Math. Anal. Appl. 472 (2019), 1458–1474. doi: 10.1016/j.jmaa.2018.12.002
  • C. Badea and L. Suciu, Hilbert space operators with two-isometric dilations, J. Oper. Theory 86(1) (2021), 93–123. doi: 10.7900/jot.2020feb05.2298
  • S. Chavan, On operators close to isometries, Studia Math. 186(3) (2008), 275–293. doi: 10.4064/sm186-3-6
  • G. Corach, A. Maestripieri, and D. Stojanoff, A classification of projectors, Topological Algebras, their Applications, and related topics, Banach Center Publications, Vol. 67, pp. 145–160, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 2005.
  • C. Foias and A.E. Frazho, The Commutant Lifting Approach to Interpolation Problems, Birkhäuser Verlag, Basel/Boston/Berlin, 1990.
  • C. Foias, A.E. Frazho, I. Gohberg, and M.A. Kaashoek, Metric Constrained Interpolation, Commutant Lifting and Systems, Birkhäuser Verlag, Basel/Boston/Berlin, 1998.
  • S. Ghara, R. Gupta, and R. Reza, Analytic m-isometries and weighted Dirichlet-type spaces, arXiv:2002.05470v2 [math.FA], 30 Apr. 2020, 1–20.
  • C.S. Kubrusly, An Introduction to Models and Decompositions in Operator Theory, Birkhäuser, Boston, 1997.
  • W. Majdak, M. Mbekhta, and L. Suciu, Operators intertwining with isometries and Brownian parts of 2-isometries, Linear Algebra Appl. 509 (2016), 168–190. doi: 10.1016/j.laa.2016.07.014
  • W. Majdak and L. Suciu, Brownian isometric parts of concave operators, New York J. Math. 25 (2019), 1067–1090.
  • W. Majdak and L. Suciu, Brownian type parts of operators in Hilbert spaces, Results Math. 75 (2020), Article no. 5. doi: 10.1007/s00025-019-1130-8
  • W. Majdak and L. Suciu, Triangulations of operators with two-isometric liftings, Integral Equations and Operator Theory 93(10) (2021), 1–24.
  • W. Majdak and L. Suciu, Convex and expansive liftings close to two-isometries and power bounded operators, Linear Algebra and its Applications 617 (2021), 1–26. doi: 10.1016/j.laa.2021.01.009
  • S. McCullough, SubBrownian operators, J. Operator Th. 22 (1989), 291–305.
  • A. Olofsson, A von Neumann-Wold decomposition of two-isometries, Acta Sci Math (Szeged) 70(3–4) (2004), 715–726.
  • S. Richter, Invariant subspaces of the Dirichlet shift, J. Reine Angew. Math. 386 (1988), 205–220.
  • S. Richter, A representation theorem for cyclic analytic two-isometries, Trans. Amer. Math. Soc. 328 (1991), 325–349. doi: 10.1090/S0002-9947-1991-1013337-1
  • S. Shimorin, Wold-type decompositions and wandering subspaces for operators close to isometries, J. Reine Angew. Math. 531 (2001), 147–189.
  • L. Suciu, Maximum subspaces related to A-contractions and quasinormal operators, J. Korean Math. Soc. 45(1) (2008), 205–219. doi: 10.4134/JKMS.2008.45.1.205
  • L. Suciu, Maximum A-isometric part of an A-contraction and applications, Israel J. Math. 174 (2009), 419–442. doi: 10.1007/s11856-009-0121-y
  • L. Suciu, On operators with two-isometric liftings, Complex Anal. Oper. Theory 14 (2020), Article no. 5. doi: 10.1007/s11785-019-00960-9
  • L. Suciu, Liftings and extensions for operators in Brownian setting, Linear and Multilinear Algebra (2020), 1–18. https://doi.org/10.1080/03081087.2020.1819948
  • L. Suciu, Operators with Brownian unitary dilations, Carpathian J. Math. 38(3) (2022), 619–630. doi: 10.37193/CJM.2022.03.08
  • B. Sz.-Nagy, C. Foias, H. Bercovici, and L. Kérchy, Harmonic Analysis of Operators on Hilbert Space, 2nd ed., Revised and enlarged edition, Universitext, Springer, New York, 2010.

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