Limit Operators And Their Applications In Operator Theory

By V. Rabinovich, S. Roch, B. Silbermann. 2004

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The Essential Norm of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions (2012, methodology): “Studying sectorial operators via their logarithms has proved to be fruitful in several ways [12,13], [15, Chapters 4,7].”
A metric approach to limit operators (2014, unknown): “See the book [12] and the paper [9] for a recent list of relevant references, and also for many examples of band-dominated operators, limit operators, and their applications.”
Convergence Analysis of the Finite Section Method and Banach Algebras of Matrices (2010, methodology): “derive necessary and sufficient conditions for the convergence of the finite section method in terms of the so-called limit operator [21].”
An affirmative answer to a core issue on limit operators (2014, background): “The basic idea in the proof presented above for Proposition 6, namely to split the domain of a band operator A into separated regions and to exploit that the action of A is limited by its band-width, has a long and successful tradition and has lead to deep results on inverse closedness and on the ex”