Brauner space

In functional analysis and related areas of mathematics Brauner space is a complete compactly generated locally convex space having a sequence of compact sets such that every other compact set is contained in some .

Brauner spaces are named after Kalman Brauner,[1] who first started to study them. All Brauner spaces are stereotype and are in the stereotype duality relations with Fréchet spaces:[2][3]

  • for any Fréchet space its stereotype dual space[4] is a Brauner space,
  • and vice versa, for any Brauner space its stereotype dual space is a Fréchet space.

Examples

Notes

  1. K.Brauner (1973).
  2. S.S.Akbarov (2003).
  3. 1 2 S.S.Akbarov (2009).
  4. The stereotype dual space to a locally convex space is the space of all linear continuous functionals endowed with the topology of uniform convergence on totally bounded sets in .

References


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