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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
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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
- 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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Category Archives: Hilbert space
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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Positive operators I
I realized that I have to diverge even more on my way to Krein spaces. We will need square roots of positive operators on real and complex Hilbert spaces, an so there is a need to discuss this subject in … Continue reading
