Operator Theory: Advances and Applications

Limit Operators and Their Applications in Operator Theory

Authors: Rabinovitch, Vladimir, Roch, Steffen, Silbermann, Bernd

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About this book

This text has two goals. It describes a topic: band and band-dominated operators and their Fredholm theory, and it introduces a method to study this topic: limit operators. Band-dominated operators. Let H = [2(Z) be the Hilbert space of all squared summable functions x : Z -+ Xi provided with the norm 2 2 X IIxl1 :=L I iI . iEZ It is often convenient to think of the elements x of [2(Z) as two-sided infinite sequences (Xi)iEZ. The standard basis of [2(Z) is the family of sequences (ei)iEZ where ei = (. . . ,0,0, 1,0,0, . . . ) with the 1 standing at the ith place. Every bounded linear operator A on H can be described by a two-sided infinite matrix (aij)i,jEZ with respect to this basis, where aij = (Aej, ei)' The band operators on H are just the operators with a matrix representation of finite band-width, i. e. , the operators for which aij = 0 whenever Ii - jl > k for some k. Operators which are in the norm closure ofthe algebra of all band operators are called band-dominated. Needless to say that band and band­ dominated operators appear in numerous branches of mathematics. Archetypal examples come from discretizations of partial differential operators. It is easy to check that every band operator can be uniquely written as a finite sum L dkVk where the d are multiplication operators (i. e.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $119.00
price for USA in USD (gross)
  • ISBN 978-3-0348-7911-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.99
price for USA in USD
  • ISBN 978-3-7643-7081-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.99
price for USA in USD
  • ISBN 978-3-0348-9619-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Limit Operators and Their Applications in Operator Theory
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
150
Copyright
2004
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-7911-8
DOI
10.1007/978-3-0348-7911-8
Hardcover ISBN
978-3-7643-7081-7
Softcover ISBN
978-3-0348-9619-1
Series ISSN
0255-0156
Edition Number
1
Number of Pages
XV, 392
Topics