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Rank-one perturbation of Toeplitz operators and reflexivity

Kliś-Garlicka K.

Opuscula Mathematica

2012

Vol. 32, no. 3

505-509

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

Approximation methods for a class of discrete Wiener-Hopf equations

Nowak M. A.

Opuscula Mathematica

2009

Vol. 29, no. 3

271-288

In this paper, we consider approximation methods for operator equations of the form Au + Bu = ƒ, where A is a discrete Wiener-Hopf operator on lp (1≤ p < ∞) which symbol has roots on the unit circle with arbitrary multiplicities (not necessary integers). Conditions on perturbation B and ƒ are given in order to guarantee the applicability of projection-iterative methods. Effective error estimates, and simultaneously, decaying properties for solutions are obtained in terms of some smooth spaces.