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Fredholm Operators and Their Generalizations

  • S. N. Krachkovskii
  • A. S. Dikanskii
Part of the Progress in Mathematics book series (PM, volume 10)

Abstract

The aim of the present article is to review the main lines of development of the theory of the (Φ-, Φ+- and Φ-operators primarily in the last ten years. A brief outline of earlier theories (Fredholm, Riesz-Schauder, Noether) affording the background for the Φ, (Φ+, Φ-operators is given in §1. In § 2 the basic results concerning the Φ, Φ+, Φ-operators in Banach spaces are presented, including the spectral and algebraic aspects of the theory. In § 3 the analogous problems in locally-convex and locally-bounded topological vector spaces are discussed. Finally, § 4 is given over to the abstract determinant theory of Fredholm. The problem area associated with the topological aspects of the theory (in the sense of K-theory [7], etc.) are not covered in the present review.

Keywords

Banach Space Closed Operator Fredholm Operator Finite Rank Fredholm Determinant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1971

Authors and Affiliations

  • S. N. Krachkovskii
  • A. S. Dikanskii

There are no affiliations available

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