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Contractive projections and Seever’s identity in complex \(f\)-algebras. (English) Zbl 1103.46024

By a result of G. L. Seever [Pac. J. Math. 17, 159–166 (1966; Zbl 0137.10002)], every positive contractive projection \(T\) on \(C_0(X)\), where \(X\) is a locally compact Hausdorff space, satisfies the identity \(T(fTg)=T(TfTg)\;(f,g\in C_0(X))\). The condition has been studied later by a number of authors. The present paper characterizes contractive projections on complex \(f\)-algebras satisfying the Seever identity.

MSC:

46H05 General theory of topological algebras
46A40 Ordered topological linear spaces, vector lattices
06F25 Ordered rings, algebras, modules

Citations:

Zbl 0137.10002
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