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- Fundamental Symmetries in Krein Spaces 2026/07/31
- Polar Decomposition and Partial Isometries 2026/07/15
- Monotone convergence for bounded self-adjoint operators 2026/07/08
- Functoriality of the Borel Functional Calculus and Pushforward of Spectral Measures 2026/07/04
- Spectral integrals and a first taste of functional calculus 2026/07/03
- 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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- Tensors are geometric objects 2025/12/10
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- Growing Out of the Sandbox 2025/12/02
- 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
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Tag Archives: real Hilbert space
Polar Decomposition and Partial Isometries
In this note I revisit the polar decomposition T=U∣T∣ for bounded (possibly antilinear) operators between Hilbert spaces, emphasizing the role of partial isometries and their initial and final subspaces. The diagram in the snow shows exactly what our polar bear … Continue reading
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Tagged antilinear, partial isometries, polar decomposition, real Hilbert space
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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
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Tagged real Hilbert space, resolution of ithe identity, spectral family
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