Mackey space

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In mathematics, particularly in functional analysis, a Mackey space is a locally convex topological vector space X such that the topology of X coincides with the Mackey topology τ(X,X′), the finest topology which still preserves the continuous dual.

Examples[edit]

Examples of Mackey spaces include:

Properties[edit]

  • A locally convex space X with continuous dual X' is a Mackey space if and only if each convex and \sigma(X', X)-relatively compact subset of X' is equicontinuous.
  • The completion of a Mackey space is again a Mackey space.[3]
  • A separated quotient of a Mackey space is again a Mackey space.
  • A Mackey space need not be separable, complete, quasi-barrelled, nor \sigma-quasi-barrelled.

References[edit]

  1. ^ a b Schaefer (1999) p. 132
  2. ^ Schaefer (1999) p. 138
  3. ^ Schaefer (1999) p. 133