Linear combinations of projections in von Neumann algebras

Goldstein, Stanisław; Paszkiewicz, Adam

doi:10.1090/S0002-9939-1992-1094501-9

Linear combinations of projections in von Neumann algebras
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by Stanisław Goldstein and Adam Paszkiewicz PDF

Proc. Amer. Math. Soc. 116 (1992), 175-183 Request permission

Abstract:

Any operator in a von Neumann algebra is a linear combination of a finite number of projections from the algebra with coefficients from the center of the algebra. Those von Neumann algebras that are the complex linear span of their projections are identified.

References

Don Deckard and Carl Pearcy, On matrices over the ring of continuous complex valued functions on a Stonian space, Proc. Amer. Math. Soc. 14 (1963), 322–328. MR 147926, DOI 10.1090/S0002-9939-1963-0147926-1
Th. Fack and P. de la Harpe, Sommes de commutateurs dans les algèbres de von Neumann finies continues, Ann. Inst. Fourier (Grenoble) 30 (1980), no. 3, 49–73 (French). MR 597017
P. A. Fillmore and D. M. Topping, Operator algebras generated by projections, Duke Math. J. 34 (1967), 333–336. MR 209855
Adam Paszkiewicz, Any selfadjoint operator is a finite linear combination of projectors, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), no. 7-8, 337–345 (1981) (English, with Russian summary). MR 628049

Self-adjoint operators as a real span of

projections

Carl Pearcy and David Topping, Commutators and certain $\textrm {II}_{1}$-factors, J. Functional Analysis 3 (1969), 69–78. MR 0239432, DOI 10.1016/0022-1236(69)90051-2
Carl Pearcy and David Topping, Sums of small numbers of idempotents, Michigan Math. J. 14 (1967), 453–465. MR 218922