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Polar Subspaces and Automatic Maximality

Abstract

This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a Banach space and its dual. In this paper, we establish several new results and also give improved proofs of some known ones in both the general and the special contexts.

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Correspondence to S. Simons.

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Simons, S. Polar Subspaces and Automatic Maximality. Set-Valued Var. Anal 22, 259–270 (2014). https://doi.org/10.1007/s11228-013-0244-5

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Keywords

  • Banach space
  • Dual and bidual
  • Maximally monotone set
  • Type (NI)
  • Subdifferential of a convex function
  • Brezis–Browder theorem
  • Rockafellar’s formula for the subdifferential of a sum
  • Brondsted–Rockafellar theorem
  • Polar subspace

Mathematics Subject Classifications (2010)

  • 47H05
  • 47A06
  • 46A20
  • 46N10
  • 47N10
  • 52A41