Infinite Matrices and Their Finite Sections: An Introduction to the Limit Operator Method

By Marko Lindner

In this book we are concerned with the study of a certain class of in?nite matrices and two important properties of them: their Fredholmness and the stability of the approximation by their ?nite truncations. Let us take these two properties as a starting point for the big picture that shall be presented in what follows. Stability Fredholmness We think of our in?nite matrices as bounded linear operators on a Banach space E of two-sided in?nite sequences. Probably the simplest case to start with 2 +? is the space E = of all complex-valued sequences u=(u ) for which m m= 2 u is summable over m? Z. m Theclassofoperatorsweareinterestedinconsistsofthoseboundedandlinear operatorsonE whichcanbeapproximatedintheoperatornormbybandmatrices. We refer to them as band-dominated operators. Of course, these considerations 2 are not limited to the space E = . We will widen the selection of the underlying space E in three directions: p - We pass to the classical sequence spaces with 1? p . n - Our elements u=(u )? E have indices m? Z rather than just m? Z. m - We allow values u in an arbitrary ?xed Banach spaceX rather than C.

• Format: Paperback
• Language: English
• ISBN: 3764377666
• ISBN13: 9783764377663
• Release Date: August 2006
• Publisher: Birkhauser
• Length: 191 Pages
• Weight: 0.85 lbs.
• Dimensions: 0.5" x 6.6" x 9.3"