The Atkinson Theorem in Hilbert <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math>-Modules over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math>-Algebras of Compact Operators

Niknam, A.; Sharifi, K.

doi:https://doi.org/10.1155/2007/53060

Abstract and Applied Analysis

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Research Article | Open Access

Volume 2007 | Article ID 053060 | https://doi.org/10.1155/2007/53060

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

A. Niknam^1,2and K. Sharifi¹

Academic Editor: Victor G. Zvyagin

Received13 Aug 2007

Accepted04 Nov 2007

Published22 Jan 2008

Abstract

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.

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Copyright

Copyright © 2007 A. Niknam and K. Sharifi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abstract and Applied Analysis

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

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