Weyl's Theorem states that for compact self-adjoint operators on a Hilbert space, the spectrum consists of eigenvalues that can accumulate only at zero. This means that the non-zero eigenvalues have finite multiplicity and the corresponding eigenspaces are finite-dimensional, establishing a critical connection between the spectral properties of compact self-adjoint operators and their behavior in functional analysis. Additionally, Weyl's Theorem plays a significant role in understanding the resolvent of bounded linear operators.
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