Index Theory for Real Factors
S. Albeverio, Sh.A. Ayupov, A.A. Rakhimov, R.A. Dadakhodjaev
TL;DR
This paper introduces an index theory for real factors, utilizing involutive *-anti-automorphisms of complex enveloping algebras, and computes the index values similarly to the complex case.
Contribution
It develops a new index theory for real factors by reducing the problem to involutive *-anti-automorphisms, extending the complex case methodology.
Findings
Index values for real factors are calculated.
Reduction of real factors to involutive *-anti-automorphisms.
Extension of complex index theory to real factors.
Abstract
The notion of index for arbitrary real factors is introduced and investigated. The main tool in our approach is the reduction of real factors to involutive *-anti-automorphisms of their complex enveloping von Neumann algebras. Similar to the complex case the values of the index for real factors are calculated.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Holomorphic and Operator Theory