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- Spectral family and resolution of the identity 2026/06/25
- Square root lemma 2026/06/17
- Positive operators II 2026/06/11
- Positive operators I 2026/06/04
- Complexification of a Real Krein Space. Part I 2026/06/01
- Pre-Hilbert space – its Dual and Completion 2026/05/29
- Fundamental Symmetries in Minkowski Krein Space 2026/05/20
- Krein spaces – a quantum-theoretical monad method 2026/05/12
- Krein spaces – first steps 2026/05/09
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- It’s all about permutations 2025/12/28
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- Blog reincarnation with analytic idealism 2025/11/30
- Minkowski patches in the Einstein universe 2025/11/27
- Floating in the Einstein Universe 2025/11/24
- Comments on Clifford algebras 2019/01/24
- Comment on “Could ordinary quantum mechanics be just fine for all practical purposes?” by Alexey Nikulov 2018/03/08
- Spinning Top – Space Odity 2017/05/28
- Geodesics of left invariant metrics on matrix Lie groups – Part 2 Conservation laws 2017/05/26
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Monthly Archives: June 2026
Spectral family and resolution of the identity
This post is (hopefully) the last one in a short series on real and complex Hilbert spaces. After this post we will return to the study of real and complex spaces with indefinite metric, Krein spaces and their geometry. In … Continue reading
Posted in Uncategorized
Tagged real Hilbert space, resolution of ithe identity, spectral family
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Square root lemma
This post is a continuation of Positive operators II, We begin by recalling the main fact proved there, then explain how a classical binomial series leads to a functional calculus for the square root of a positive operator. Corollary 1 … Continue reading
Posted in Functional analysis, Hilbert space
Tagged Hilbert space, positive operator, positive square root
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Positive operators II
This post is a continuation of Positive operators I. The aim here is to explain how the norm of a bounded self–adjoint operator can be expressed in terms of the associated quadratic form. We will first recall the Riesz representation … Continue reading
Posted in Functional analysis, Hilbert space
Tagged bilinear functional, Hilbert space, positive operators
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