A Von Neumann Algebra over the Adele Ring and the Euler Totient Function

Ilwoo Cho () and Palle E. T. Jorgensen ()
Additional contact information
Ilwoo Cho: St. Ambrose University, Department of Mathematics
Palle E. T. Jorgensen: The University of Iowa, Department of Mathematics

Chapter 45 in Operator Theory, 2015, pp 1285-1335 from Springer

Abstract: Abstract In this chapter, relations between calculus on a von Neumann algebra 𝔐 ℚ $$\mathfrak{M}_{\mathbb{Q}}$$ over the Adele ring 𝔸 ℚ $$\mathbb{A}_{\mathbb{Q}}$$ , and free probability on a certain subalgebra Φ $$\Phi $$ of the algebra 𝒜 , $$\mathcal{A},$$ consisting of all arithmetic functions equipped with the functional addition and convolution are studied. By showing that the Adelic calculus over 𝔸 ℚ $$\mathbb{A}_{\mathbb{Q}}$$ is understood as a free probability on a certain von Neumann algebra 𝔐 ℚ $$\mathfrak{M}_{\mathbb{Q}}$$ , the connections with a system of natural free-probabilistic models on the subalgebra Φ $$\Phi $$ in 𝒜 $$\mathcal{A}$$ are considered. In particular, the subalgebra Φ $$\Phi $$ is generated by the Euler totient function ϕ.

Date: 2015
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0667-1_45

Ordering information: This item can be ordered from
http://www.springer.com/9783034806671

DOI: 10.1007/978-3-0348-0667-1_45

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().