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Topologies on central extensions of von Neumann algebras

100%
Ayupov S., Kudaybergenov K., Djumamuratov R.
Open Mathematics
|
2012
|
tom 10
|
nr 2
656-664
EN
Given a von Neumann algebra M, we consider the central extension E(M) of M. We introduce the topology t c(M) on E(M) generated by a center-valued norm and prove that it coincides with the topology of local convergence in measure on E(M) if and only if M does not have direct summands of type II. We also show that t c(M) restricted to the set E(M)h of self-adjoint elements of E(M) coincides with the order topology on E(M)h if and only if M is a σ-finite type Ifin von Neumann algebra.
2
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Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs

60%
Cho I., Jorgensen P. E. T.
Special Matrices
|
2015
|
tom 3
|
nr 1
EN
In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the algebra A of all arithmetic functions, we establish a corresponding subalgebra AG = C*[α(G)]︀ of A. We construct a suitable representation of AG, determined both by G and by an arbitrarily fixed prime p. And then based on this representation, we consider free probability on AG.
3
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Matrices induced by arithmetic functions acting on certain Krein spaces

53%
Cho I.
Special Matrices
|
2017
|
tom 5
|
nr 1
258-289
EN
In this paper, we study matrices induced by arithmetic functions under certain Krein-space representations induced by (multi-)primes less than or equal to fixed positive real numbers.
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