The Atkinson Theorem in Hilbert C*-Modules Over C*-Algebras of Compact Operators

Assadollah Niknam; Kamran Sharifi

doi:10.1155/2007/53060

The Atkinson Theorem in Hilbert C-Modules Over C-Algebras of Compact Operators

Operator Algebras 2015-06-26 v3 Functional Analysis

Authors: Assadollah Niknam , Kamran Sharifi

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Abstract

In this paper the concept of unbounded Fredholm operators on Hilbert C*- modules over an arbitrary C*-algebra is discussed and the Atkinson theorem is generalized for bounded and unbounded Feredholm operators on Hilbert C*-modules over C*-algebras of compact operators. In the framework of Hilbert C*-modules over C*-algebras of compact operators, the index of an unbounded Fredholm operator and the index of its bounded transform are the same.

Keywords

Hilbert C*-modules C*-algebras of compact operators Fredholm operators Atkinson theorem index bounded transform

Cite

@article{arxiv.math/0611916,
  title  = {The Atkinson Theorem in Hilbert C*-Modules Over C*-Algebras of Compact Operators},
  author = {Assadollah Niknam and Kamran Sharifi},
  journal= {arXiv preprint arXiv:math/0611916},
  year   = {2015}
}

Comments

8 pages, the proof of the Theorem 2.3 was omitted, to appear in Abstract and Applied Analysis