论文信息 - The Mackey-Gleason Problem

The Mackey-Gleason Problem

Let A be a von Neumann algebra with no direct summand of Type I 2 , and let P(A) be its lattice of projections. Let X be a Banach space. Let m:P(A)→X be a bounded function such that m(p+q)=m(p)+m(q) whenever p and q are orthogonal projections. The main theorem states that m has a unique extension to a bounded linear operator from A to X. In particular, each bounded complex-valued finitely additive quantum measure on P(A) has a unique extension to a bounded linear functional on A

J. Wright | J. D. Maitland Wright | L. J. Bunce | L. Bunce

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