Quantum structures and operator algebras

Hamhalter, Jan

doi:10.1016/b978-044452870-4/50029-7

Cited by 4 publications

(2 citation statements)

References 113 publications

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“…It is worth mentioning that the idea of using L p space has been previously proposed in the foundations of quantum physics; see, e.g., [21,25,44,53]. Instead of these simplicity arguments, we can simply say that the empirical observation confirms that p = |ψ| 2 as in Feynman path integration but not that p = |ψ| 4 or p = |ψ| 6 etc., as in possible alternative theories.…”

Section: Physical Commentsmentioning

confidence: 98%

Algorithmic Aspects of Analysis, Prediction, and Control in Science and Engineering

Nava¹,

Kreinovich²

2015

Studies in Systems, Decision and Control

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The series "Studies in Systems, Decision and Control" (SSDC) covers both new developments and advances, as well as the state of the art, in the various areas of broadly perceived systems, decision making and control-quickly, up to date and with a high quality. The intent is to cover the theory, applications, and perspectives on the state of the art and future developments relevant to systems, decision making, control, complex processes and related areas, as embedded in the fields of engineering, computer science, physics, economics, social and life sciences, as well as the paradigms and methodologies behind them. The series contains monographs, textbooks, lecture notes and edited volumes in systems, decision making and control spanning the areas of Cyber-Physical SystemsSocial Systems, Economic Systems and other. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution and exposure which enable both a wide and rapid dissemination of research output.More information about this series at

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Section: Physical Commentsmentioning

confidence: 98%

Algorithmic Aspects of Analysis, Prediction, and Control in Science and Engineering

Nava¹,

Kreinovich²

2015

Studies in Systems, Decision and Control

View full text Add to dashboard Cite

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“…There is a vast literature on this subject and we refer the interested reader to main monographs [1][2][3][4] and references therein. Subspace structures of inner product spaces are important for axiomatization program in quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Subspace Structures in Inner Product Spaces and von Neumann Algebras

Hamhalter

Turilova

2011

Int J Theor Phys

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We study subspaces of inner product spaces that are invariant with respect to a given von Neumann algebra. The interplay between order properties of the poset of affiliated subspaces and the structure of a von Neumann algebra is investigated. We extend results on nonexistence of measures on incomplete structures to invariant subspaces. Results on inner product spaces as well as on the structure of affiliated subspaces are reviewed.

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Affiliated subspaces and infiniteness of von Neumann algebras

Hamhalter

Turilova

2013

Mathematische Nachrichten

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We show that the structural properties of von Neumann algebra s are connected with the metric and order theoretic properties of various classes of affiliated subspaces. Among others we show that properly infinite von Neumann algebra s always admit an affiliated subspace for which (1) closed and orthogonally closed affiliated subspaces are different; (2) splitting and quasi‐splitting affiliated subspaces do not coincide. We provide an involved construction showing that concepts of splitting and quasi‐splitting subspaces are non‐equivalent in any GNS representation space arising from a faithful normal state on a Type I factor. We are putting together the theory of quasi‐splitting subspaces developed for inner product spaces on one side and the modular theory of von Neumann algebra s on the other side.

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Quantum structures and operator algebras

Cited by 4 publications

References 113 publications

Algorithmic Aspects of Analysis, Prediction, and Control in Science and Engineering

Algorithmic Aspects of Analysis, Prediction, and Control in Science and Engineering

Subspace Structures in Inner Product Spaces and von Neumann Algebras

Affiliated subspaces and infiniteness of von Neumann algebras

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