Order units in a C*-algebra
classification
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keywords
algebraorderpropertycharacterizeddefinedelementhereditarypositive
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Order unit property of a positive element in a $C^{*}$-algebra is defined. It is proved that precisely projections satisfy this order theoretic property. This way, unital hereditary $C^{*}$-subalgebras of a $C^{*}$-algebra are characterized.
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