Infinite norm decompositions of C$^*$-algebras
Farkhad Arzikulov

TL;DR
This paper explores the concept of infinite norm decomposition in C$^*$-algebras, demonstrating that such decompositions yield new C$^*$-algebras and constructing examples of factors and purely infinite algebras.
Contribution
It introduces the notion of infinite norm decomposition for C$^*$-algebras and proves that these decompositions form new C$^*$-algebras, expanding the understanding of their structure.
Findings
Infinite norm decomposition of any C$^*$-algebra is itself a C$^*$-algebra.
Constructed examples of C$^*$-factors with infinite and nonzero finite projections.
Constructed simple purely infinite C$^*$-algebras.
Abstract
In the given article the notion of infinite norm decomposition of a C-algebra is investigated. The norm decomposition is some generalization of Peirce decomposition. It is proved that the infinite norm decomposition of any C-algebra is a C-algebra. C-factors with an infinite and a nonzero finite projection and simple purely infinite C-algebras are constructed.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Deception detection and forensic psychology · Advanced Operator Algebra Research
