A second look at "A Geometric Proof of the Spectral Theorem for Unbounded Self-Adjoint Operators"

2017/12/21 by Herbert Leinfelder, Leinfelder, Herbert
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1712.07988

openalex publication_date 2017/12/21 · openalex created_date 2018/01/05 · openalex updated_date 2026/07/28

Abstract

A new geometric proof of the spectral theorem for unbounded self-adjoint operators A in a Hilbert space H is given based on a splitting of A in positive and negative parts A+ and A-. For both operators A+ and A- the spectral family can be defined immediately and then put together to become the spectral family of A.

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