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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
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- Blog reincarnation with analytic idealism 2025/11/30
- Minkowski patches in the Einstein universe 2025/11/27
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- 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: Hilbert space
Monotone convergence for bounded self-adjoint operators
I realized that before the Square Root Lemma post, I should have included a short section. Here is this section. The following Lemma is often being used in the construction of the square root of a self-adjoint positive operator. We … Continue reading
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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