States and Representations

Lars Tuset
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Lars Tuset: Oslo Metropolitan University, Department of Computer Science

Chapter Chapter 6 in Analysis and Quantum Groups, 2022, pp 169-191 from Springer

Abstract: Abstract A positive linear functional on a C∗-algebra is one that takes positive elements to non-negative numbers. They are automatically bounded, and among these, are exactly the ones that attain their norm at the unit, or in the non-unital case, attain it as the limit evaluated at any approximative unit; such ‘units’ always exist. Any bounded linear functional can be written as a difference of two positive functionals, which in the commutative case amounts to the Jordan decomposition of the corresponding complex measure.

Date: 2022
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DOI: 10.1007/978-3-031-07246-8_6

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