Linear Combinations of Projections in Type III Factors

Author:

Goldstein StanisławORCID,Paszkiewicz AdamORCID

Abstract

AbstractIt is shown that every self-adjoint operator in a $$\sigma $$ σ -finite von Neumann factor of type III can be written as a real linear combination of 3 projections. This is in stark contrast to factors of type $$I_\infty ,\, II_1$$ I , I I 1 and $$II_\infty $$ I I , where there are always operators that require at least 4 projections in such a representation.

Publisher

Springer Science and Business Media LLC

Subject

Algebra and Number Theory,Analysis

Reference17 articles.

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3. Marcoux, L.W.: On the linear span of the projections in certain simple $$C^*$$-algebras. Indiana Univ. Math. J. 51(3), 753–771 (2002)

4. Marcoux, L.W.: Sums of small number of commutators. J. Operator Theory 56(1), 111–142 (2006)

5. Kaftal, V., Ng, P.W., Zhang, S.: Projections in $$C^*$$-algebras and strict comparison. In: Operator theory: the state of the art, volume 18 of Theta Ser. Adv. Math., pp. 53–74. Theta, Bucharest, (2016)

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