Rank-one perturbation of Toeplitz operators and reflexivity

• Autorzy: Kliś-Garlicka K.
• Języki publikacji: EN

Abstrakty

EN

It was shown that rank-one perturbation of the space of Toeplitz operators preserves 2-hyperreflexivity.

Słowa kluczowe

EN

Toeplitz operators; reflexivity; hyperreflexivity

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2012
• Tom: Vol. 32, no. 3
• Strony: 505--509
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Kliś-Garlicka K.

• University of Agriculture, Institute of Mathematics, Balicka 253c, 30-198 Kraków, Poland,

Bibliografia

• [1] N.T. Arveson, Interpolation problems in nest algebras, J. Funct. Anal. 20 (1975), 208–233.
• [2] N.T. Arveson, Ten lectures on operator algebras, CBMS Regional Conference Series 55, Amer. Math. Soc., Providence, 1984.
• [3] E.A. Azoff, On finite rank operators and preannihilators, Mem. Amer. Math. Soc. 64 (1986).
• [4] E.A. Azoff, M. Ptak, A dichotomy for linear spaces of Toeplitz operators, J. Funct. Anal. 156 (1998), 411–428.
• [5] H. Bercovici, C. Foias, C. Pearcy, Dual algebras with applications to invariant subspaces and dilation theory, CBMS Reg. Conf. Ser. Math. 56, Amer. Math. Soc., Providence, 1985.
• [6] J. Bourgain, A problem of Douglas and Rudin on factorization, Pacific J. Math. 121 (1986), 47–50.
• [7] J.B. Conway, A course in operator theory, Amer. Math. Soc., Providence, 2000.
• [8] K. Davidson, The distance to the analytic Toeplitz operators. Illinois J. Math 31 (1987) 2, 265–273.
• [9] P.R. Halmos, A Hilbert space problem book, Van Nostrand, Princeton, NJ, 1967.
• [10] K. Klis, M. Ptak, k-hyperreflexive subspaces, Houston J. Math. 32 (2006), 299–313.
• [11] J. Kraus, D. Larson, Some applications of a technique for constructing reflexive operator algebras. J. Operator Theory 13 (1985), 227–236.
• [12] J. Kraus, D. Larson, Reflexivity and distance formulae, Proc. Lond. Math. Soc. 53 (1986), 340–356.
• [13] D. Larson, Annihilators of operator algebras, Operator Theory 6 (1982), 119–130.
• [14] W.E. Longstaff, On the operation Alg Lat in finite dimensions, Linear Algebra Appl. 27 (1979), 27–29.
• [15] H. Mustafayev, On hyper-reflexivity of some operator spaces, Int. J. Math. Math. Sci. 19 (1996), 603–606.