Helly, Hahn-Banach analytic form(FASSPDE)

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Theorem 1.1 Helly, Hahn-Banach analytic form

Result

Hahn-Banach Theorem admits an extension of the linear functional on a linear subspace to the whole space which is bounded by a maximal element admitted by the Zorn’s Lemma.

Proof(See Appendix Above)

Hahn-Banach Theorem admits an extension of the linear functional on a linear Subspace to the whole space which is bounded by a maximal element admitted by the Zorn’s Lemma.

Reference

Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Chapter 1

Related Topics

  • Definitions
    • Vector Space
    • Positive Homogeneous
    • Additive(subadditive)
    • Linear Space
    • Linear Functional
  • Theorems/Corollary/Propositions/Lemmas

Corollary 1.1.1

Statement

Result

This corollary makes it possible for the norm in the whole space of the extension of g into the subspace where g is in, and the equality always hold.

Reference

Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Chapter 1

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Corollary 1.1.2

Statement

Remark

Reference

Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Chapter 1

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Corollary 1.1.3

Statement

Remark

Reference

Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Chapter 1

Related Topics