Theorem (Analytic Fredholm Alternative)Let be a connected open subset of and be a separable Hilbert space. Suppose that is an analytic operator-valued function such that is compact . Then either

- does not exist .
- exists , where is discrete.

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# Tag: Fredholm Alternative

# Fredholm Alternative and Riesz Schauder Theorem

Theorem (Analytic Fredholm Alternative)Let be a connected open subset of and be a separable Hilbert space. Suppose that is an analytic operator-valued function such that is compact . Then either

- does not exist .
- exists , where is discrete.