Perturbation of Toeplitz operators and reflexivity

Kamila Kliś-Garlicka

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2014)

  • Volume: 13, page 15-18
  • ISSN: 2300-133X

Abstract

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It was shown that the space of Toeplitz operators perturbated by finite rank operators is 2-hyperreflexive.

How to cite

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Kamila Kliś-Garlicka. "Perturbation of Toeplitz operators and reflexivity." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 13 (2014): 15-18. <http://eudml.org/doc/268927>.

@article{KamilaKliś2014,
abstract = {It was shown that the space of Toeplitz operators perturbated by finite rank operators is 2-hyperreflexive.},
author = {Kamila Kliś-Garlicka},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {reflexive; k-hyperreflexive; finite rank operator; perturbated},
language = {eng},
pages = {15-18},
title = {Perturbation of Toeplitz operators and reflexivity},
url = {http://eudml.org/doc/268927},
volume = {13},
year = {2014},
}

TY - JOUR
AU - Kamila Kliś-Garlicka
TI - Perturbation of Toeplitz operators and reflexivity
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2014
VL - 13
SP - 15
EP - 18
AB - It was shown that the space of Toeplitz operators perturbated by finite rank operators is 2-hyperreflexive.
LA - eng
KW - reflexive; k-hyperreflexive; finite rank operator; perturbated
UR - http://eudml.org/doc/268927
ER -

References

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  1. [1] N.T. Arveson, Interpolation problems in nest algebras, J. Funct. Anal. 20 (1975), 208-233. Cited on 17.[Crossref] 
  2. [2] N.T. Arveson, Ten lectures on operator algebras, CBMS Regional Conference Series in Mathematics 55, Amer. Math. Soc., Providence (1984). Cited on 16. 
  3. [3] E.A. Azoff, M. Ptak, A dichotomy for linear spaces of Toeplitz operators, J. Funct. Anal. 156 (1998), 411-428. Cited on 16.[Crossref] 
  4. [4] K. Davidson, The distance to the analytic Toeplitz operators, Illinois J. Math. 31 (1987), 265-273. Cited on 17. 
  5. [5] P.R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London 1967. Cited on 16. 
  6. [6] K. Klis-Garlicka, Rank-one perturbation of Toeplitz operators and reflexivity, Opuscula Math. 32 (2012), 505-509. Cited on 15 and 16. 
  7. [7] K. Klis, M. Ptak, k-hyperreflexive subspaces, Houston J. Math. 32 (2006), 299-313. Cited on 16 and 17. 
  8. [8] J. Kraus, D. Larson, Some applications of a technique for constructing reflexive operator algebras, J. Operator Theory, 13 (1985), 227-236. Cited on 16. 
  9. [9] J. Kraus, D. Larson, Reflexivity and distance formulae, Proc. London Math. Soc. 53 (1986), 340-356. Cited on 15 and 16. 
  10. [10] W.E. Longstaff, On the operation Alg Lat in finite dimensions, Linear Algebra Appl. 27 (1979), 27-29. Cited on 15.[Crossref] 
  11. [11] H. Mustafayev, On hyper-reflexivity of some operator spaces, Internat. J. Math. Math. Sci., 19 (1996), 603-606. Cited on 17.[Crossref] 

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