Notes on the universal determinant bundle
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چکیده
1.1 (Fredholm operators). Let X, Y be real Banach spaces and denote their dual spaces by X, Y . A bounded linear operator D : X → Y is called Fredholm if it has a closed image and if its kernel and cokernel (the quotient space Y/imD) are finite dimensional. Equivalently, there exists a bounded linear operator T : Y → X such that the operators TD− idX and DT − idY are compact. The Fredholm index of a Fredholm operator D : X → Y is the integer index(D) := dim(ker D)− dim(cokerD).
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