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In the context of von Neumann algebras, the central carrier of a projection ''E'' is the smallest central projection, in the von Neumann algebra, that dominates ''E''. It is also called the central support or central cover. == Definition == Let ''L''(''H'') denote the bounded operators on a Hilbert space ''H'', M ⊂ ''L''(''H'') be a von Neumann algebra, and M` the commutant of M. The center of M is ''Z''(M) = M` ∩ M = . The central carrier ''C''(''E'') of a projection ''E'' in M is defined as follows: :''C''(''E'') = ∧ . The symbol ∧ denotes the lattice operation on the projections in ''Z''(M): ''F''1 ∧ ''F''2 is the projection onto the closed subspace Ran(''F''1) ∩ Ran(''F''2). The abelian algebra ''Z''(M), being the intersection of two von Neumann algebras, is also a von Neumann algebra. Therefore ''C''(''E'') lies in ''Z''(M). If one think of M as a direct sum (or more accurately, a direct integral) of its factors, then the central projections are the projections that are direct sums (direct integrals) of identity operators of (measurable sets of) the factors. If ''E'' is confined to a single factor, then ''C''(''E'') is the identity operator in that factor. Informally, one would expect ''C''(''E'') to be the direct sum of identity operators ''I'' where ''I'' is in a factor and '' I · E ≠ 0''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Central carrier」の詳細全文を読む スポンサード リンク
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