Ideals of Projections According to σ-Algebras and Unbounded Measurements-Reference-Cited by-同舟云学术

Ideals of Projections According to σ-Algebras and Unbounded Measurements

Published:2023-02-07 Issue:2 Volume:12 Page:167
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Matvejchuk Marjan¹^ORCID

Affiliation:

1. Department of Theoretical and Applied Mechanics and Mathematics, Kazan National Research Technical University, ul. Karla Marksa, 10, Kazan 420111, Russia

Abstract

A theory of unbounded measures is constructed based on the quantum logics of orthogonal projections. As an analogue of the ring of sets, the projector ideal is proposed. Finite and maximal measures regarding the projector ideals are described. Analogues of a number of classical theorems of measure theory are found. A wide class of unbounded measures on projection ideals is characterized. A number of sufficient conditions are found to extend unbounded measures to an integral of the entire algebra. The problem of describing unbounded σ-finite measures in semifinite algebras using von Neumann is similar to the Gleason problem.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/2/167/pdf

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