Definition of "subspaces" [subspaces]

• Plural form of subspace. (noun)

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• "(An irreducible representation is one in which there are no subspaces invariant under the group action, apart from the null vector and the entire Hilbert space)."
• "If the state space of an elementary system had relativistically invariant subspaces then it would be appropriate to associate these subspaces with elementary systems."
• "Put more technically, the state space of an elementary system must not contain any relativistically invariant subspaces, i.e., it must be the state space of an irreducible representation of the relevant invariance group."