The Atkinson theorem in Hilbert \(C^{\ast}\)-modules over \(C^{\ast}\)-algebras of compact operators. (English) Zbl 1155.46026

Summary: The concept of unbounded Fredholm operators on Hilbert \(C^{\ast}\)-modules over an arbitrary \(C^{\ast}\)-algebra is discussed and the Atkinson theorem is generalized for bounded and unbounded Fredholm operators on Hilbert \(C^{\ast}\)-modules over \(C^{\ast}\)-algebras of compact operators. In the framework of Hilbert \(C^{\ast}\)-modules over \(C^{\ast}\)-algebras of compact operators, the index of an unbounded Fredholm operator and the index of its bounded transform are the same.


46L08 \(C^*\)-modules
47A53 (Semi-) Fredholm operators; index theories
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