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On Universal Operators and Universal Pairs

  • Riikka Schroderus (a1) and Hans-Olav Tylli (a1)
Abstract

We study some basic properties of the class of universal operators on Hilbert spaces, and provide new examples of universal operators and universal pairs.

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1.Caradus, S. R., Universal operators and invariant subspaces, Proc. Amer. Math. Soc. 23 (1969), 526527.
2.Caradus, S. R., Pfaffenberger, W. E. and Yood, Bertram, Calkin algebras and algebras of operators on Banach spaces, Lecture Notes in Pure and Applied Mathematics, Volume 9 (Marcel Dekker, New York, 1974).
3.Chalendar, I. and Partington, J. R., Modern approaches to the invariant-subspace problem, Cambridge Tracts in Mathematics, Volume 188 (Cambridge University Press, Cambridge, 2011).
4.Cowen, C. C. and Gallardo-Gutiérrez, E. A., Unitary equivalence of one-parameter groups of Toeplitz and composition operators, J. Funct. Anal. 261(9) (2011), 26412655.
5.Cowen, C. C. and Gallardo-Gutiérrez, E. A., Consequences of universality among Toeplitz operators, J. Math. Anal. Appl. 432(1) (2015), 484503.
6.Cowen, C. C. and Gallardo-Gutiérrez, E. A., An introduction to Rota's universal operators: properties, old and new examples and future issues, Concr. Oper. 3 (2016), 4351.
7.Cowen, C. C. and Gallardo-Gutiérrez, E. A., Rota's universal operators and invariant subspaces in Hilbert spaces, J. Funct. Anal. 271(5) (2016), 11301149.
8.Cowen, C. C. and Gallardo-Gutiérrez, E. A., A new proof of a Nordgren, Rosenthal and Wintrobe theorem on universal operators, In Problems and recent methods in operator theory (eds Bothelho, F., King, R. and Rao, T.S.S.R.K.), pp. 97102, Contemporary Mathematics, Volume 687 (American Mathematical Society, Memphis, TN, 2017).
9.Cowen, C. C. and MacCluer, B. D., Composition operators on spaces of analytic functions, Studies in Advanced Mathematics (CRC Press, Boca Raton, FL, 1995).
10.Elliott, S. and Jury, M. T., Composition operators on Hardy spaces of a half-plane, Bull. Lond. Math. Soc. 44(3) (2012), 489495.
11.Elliott, S. J. and Wynn, A., Composition operators on weighted Bergman spaces of a half-plane, Proc. Edinb. Math. Soc. (2) 54(2) (2011), 373379.
12.Gallardo-Gutiérrez, E. A. and Gorkin, P., Minimal invariant subspaces for composition operators, J. Math. Pures Appl. (9) 95(3) (2011), 245259.
13.Gallardo-Gutiérrez, E. A. and Schroderus, R., The spectra of linear fractional composition operators on weighted Dirichlet spaces, J. Funct. Anal. 271(3) (2016), 720745.
14.Heller, K., Adjoints of linear fractional composition operators on S2(𝔻), J. Math. Anal. Appl. 394(2) (2012), 724737.
15.Higdon, W. M., The spectra of composition operators from linear fractional maps acting upon the Dirichlet space, J. Funct. Anal. 220(1) (2005), 5575.
16.Hurst, P. R., Relating composition operators on different weighted Hardy spaces, Arch. Math. (Basel) 68(6) (1997), 503513.
17.Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces I: sequence spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Volume 92 (Springer-Verlag, Berlin–New York, 1977).
18.Matache, V., On the minimal invariant subspaces of the hyperbolic composition operator, Proc. Amer. Math. Soc. 119(3) (1993), 837841.
19.Matache, V., Composition operators on Hardy spaces of a half-plane Proc. Amer. Math. Soc. 127(5) (1999), 14831491.
20.Matache, V., Invertible and normal composition operators on the Hilbert Hardy space of a half–plane, Concr. Oper. 3 (2016), 7784.
21.Müller, V., Spectral theory of linear operators and spectral systems in Banach algebras, Operator Theory: Advances and Applications, Volume 139 (Birkhäuser Verlag, Basel, 2003).
22.Müller, V., Universal n-tuples of operators, Math. Proc. R. Ir. Acad. 113A(2) (2013), 143150.
23Murphy, G. J., C*-Algebras and operator theory (Academic Press, Boston, MA, 1990).
24.Nordgren, E., Rosenthal, P. and Wintrobe, F. S., Invertible composition operators on H p, J. Funct. Anal. 73(2) (1987), 324344.
25.Partington, J. R. and Pozzi, E., Universal shifts and composition operators, Oper. Matrices 5(3) (2011), 455467.
26.Pozzi, E., Universality of weighted composition operators on L 2([0, 1]) and Sobolev spaces, Acta Sci. Math. (Szeged) 78(3–4) (2012), 609642.
27.Rosenblum, M. and Rovnyak, J., Hardy classes and operator theory. Corrected reprint of the 1985 original (Dover Publications, Mineola, NY, 1997).
28.Rota, G. C., Note on the invariant subspaces of linear operators, Rend. Circ. Mat. Palermo (2) 8 (1959), 182184.
29.Rudin, W., Real and complex analysis, 3rd edn (McGraw-Hill, New York, 1987).
30.Schroderus, R., Spectra of linear fractional composition operators on the Hardy and weighted Bergman spaces of the half-plane, J. Math. Anal. Appl. 447(2) (2017), 817833.
31.Shapiro, J. H., Composition operators and classical function theory. Universitext: Tracts in Mathematics (Springer-Verlag, New York, 1993).
32.Zorboska, N., Composition operators on S a spaces, Indiana Univ. Math. J. 39(3) (1990), 847857.
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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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