Convergence of observables on quantum logics

Foundations of Physics 20 (4):417-434 (1990)
  Copy   BIBTEX


We define two types of convergence for observables on a quantum logic which we call M-weak and uniform M-weak convergence. These convergence modes correspond to weak convergence of probability measures. They are motivated by the idea that two (in general unbounded) observables are “close” if bounded functions of them are “close.” We show that M-weak and uniform M-weak convergence generalize strong resolvent and norm resolvent convergence for self-adjoint operators on a Hilbert space. Also, these types of convergence strengthen the weak operator convergence and operator norm convergence of bounded self-adjoint operators on a Hilbert space. Finally, we consider spectral perturbation by showing that the spectra of approximating observables approach the spectrum of the limit in a certain sense



    Upload a copy of this work     Papers currently archived: 76,168

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Functional properties and convergence in biology.Mark B. Couch - 2005 - Philosophy of Science 72 (5):1041-1051.
On the observables on quantum logics.S. Pulmannová - 1981 - Foundations of Physics 11 (1-2):127-136.
Strong convergence in finite model theory.Wafik Boulos Lotfallah - 2002 - Journal of Symbolic Logic 67 (3):1083-1092.
Logical Aspects of Rates of Convergence in Metric Spaces.Eyvind Martol Briseid - 2009 - Journal of Symbolic Logic 74 (4):1401 - 1428.
Mereology on Topological and Convergence Spaces.Daniel R. Patten - 2013 - Notre Dame Journal of Formal Logic 54 (1):21-31.
Open questions in the ethics of convergence.George Khushf - 2007 - Journal of Medicine and Philosophy 32 (3):299 – 310.
Lebesgue Convergence Theorems and Reverse Mathematics.Xiaokang Yu - 1994 - Mathematical Logic Quarterly 40 (1):1-13.


Added to PP

17 (#640,852)

6 months
1 (#448,551)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references