Topological Vector Spaces

Schaefer, H. H., & Wolff, M. P. (1999). Topological Vector Spaces. Springer.

Type

Book

Intellectual base

Review or monograph

Year

1999

DOI

10.1007/978-1-4612-1468-7

ISBN

9781461271550

Link

https://doi.org/10.1007/978-1-4612-1468-7

Cited by

8 citations across 8 artifacts.

Domain-specific

• Brauner space
  • … transfers from The continuous dual of C(M) for a sigma-compact locally compact space M, interpreted as compactly supported Radon measures with the appropriate dual topology, is a Brauner space. to Compactly supported distributions on a smooth manifold provide Brauner-type duals of Fréchet spaces of smooth functions..
• Countably quasi-barrelled space
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• DF-space
  • DF in distribution notation, data-frame software, and other acronym expansions are unrelated.
• Dual System
  • Thus (Y) embeds into the algebraic dual of (X), and (X) embeds into the algebraic dual of (Y), without requiring either to be the other's entire algebraic dual.
• Fréchet space
  • A Fréchet space is a complete, metrizable, locally convex topological vector space under the prevailing convention; authors who omit local convexity generally use the term F-space.
• Nuclear operators between Banach spaces
  • Nuclearity depends on Banach spaces and summability convention, representations are nonunique and traces require approximation-property or stronger nuclearity hypotheses.
• Schwartz topological vector space
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Topological homomorphism
  • Continuity alone does not make a linear map a topological homomorphism: the image topology must agree with the quotient topology, equivalently the map is open onto its range under standard definitions.

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