Functional Analysis

Walter Rudin, F. (1991). Functional Analysis. McGraw-Hill.

Type

Book chapter

Intellectual base

Textbook

Year

1991

ISBN

9780070542365

Link

https://openlibrary.org/books/OL1853956Mmatched

Cited by

5 citations across 5 artifacts.

Domain-specific

• C space
  • … distinction between constitutive identity and a convenient observable transfers from The sequence (1+1/n) belongs to c and converges to 1 but does not belong to c0. to Arguments distinguish c from the space of continuous functions often denoted C and track the nonzero limit component when comparing its dual with l1..
• Fréchet space
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Fundamental theorem of Hilbert spaces
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Space of continuous functions on a compact space
  • … scalar function on the interval and is complete in \(\lVert\cdot\rVert_\infty\). to For compact Hausdorff \(X\), every continuous linear functional on \(C(X)\) is represented by integration against a finite regular signed or complex Borel measure under the Riesz–Markov–Kakutani theorem. demonstrates that continuity.
• Total subset
  • A total subset provides enough vectors to approximate every point of the ambient topological vector space by finite linear combinations.

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