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October 16, 2025Open Access

Transfinite Iteration of Operator Transforms and Spectral Projections in Hilbert and Banach Spaces

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Ordinal-indexed iterations achieved convergence to spectral projections in Hilbert and Banach spaces, indicating broader applications.

Convergence to spectral projections is proven under specific functional-calculus conditions, enhancing analyses.
Multi-layer iterations for normal operators yield strong operator topology convergence to joint peripheral fixed sets.
Reflexive Banach spaces show mean-ergodic projections yielding operators under a peripheral-separation condition.
Explicit two-layer Schur filters and examples illustrate concrete applications and potential limitations effectively.

Alpay et al. (2025) studied this question.

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