Perturbation of Toeplitz operators and reflexivity

Kamila Kliś-Garlicka

Abstract


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

Keywords


reflexivity, hyperreflexivity, Toeplitz operators

Mathematics Subject Classification (2010)


47A15, 47L99

References


Arveson, N.T. "Interpolation problems in nest algebras." J. Funct. Anal. 20 (1975): 208-233.

---. "Ten lectures on operator algebras." CBMS Regional Conference Series in Mathematics 55. Providence: Amer. Math. Soc., 1984.

Azoff E.A. and M. Ptak. "A dichotomy for linear spaces of Toeplitz operators." J. Funct. Anal. 156 (1998): 411-428.

Davidson, K. "The distance to the analytic Toeplitz operators." Illinois J. Math. 31 (1987): 265-273.

Halmos, P.R. "A Hilbert space problem book." Princeton, N.J.-Toronto, Ont.-London: D. Van Nostrand Co., Inc., 1967.

Kliś-Garlicka, K. "Rank-one perturbation of Toeplitz operators and reflexivity." Opuscula Math. 32 (2012): 505-509.

Kliś K. and M. Ptak. "k-hyperreflexive subspaces." Houston J. Math. 32 (2006): 299-313.

Kraus, J. and D. Larson. "Some applications of a technique for constructing reflexive operator algebras." J. Operator Theory, 13 (1985): 227-236.

---. "Reflexivity and distance formulae." Proc. London Math. Soc. 53 (1986): 340-356.

Longstaff, W.E. "On the operation Alg Lat in finite dimensions." Linear Algebra Appl. 27 (1979): 27–29.

Mustafayev, H. "On hyper-reflexivity of some operator spaces." Internat. J. Math. Math. Sci., 19 (1996): 603-606.


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