Infrabarreled space

In functional analysis, a locally convex topological vector space (TVS) is said to be infrabarreled if every bounded absorbing barrel is a neighborhood of the origin.[1]

Properties

Examples
  • Every barreled space is infrabarreled.[1]
  • Every product and locally convex direct sum of any family of infrabarreled spaces is infrabarreled.[2]
  • Every separated quotient of an infrabarreled space is infrabarreled.[2]

A closed vector subspace of an infrabarreled space is, however, not necessarily infrabarreled.[2]

See also
  • Barreled space

References
  1. Schaefer 1999, p. 142.
  2. Schaefer 1999, p. 194.
  • Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.CS1 maint: ref=harv (link)
  • Trèves, François (August 6, 2006) [1967]. Topological Vector Spaces, Distributions and Kernels. Mineola, N.Y.: Dover Publications. ISBN 978-0-486-45352-1. OCLC 853623322.CS1 maint: ref=harv (link) CS1 maint: date and year (link)
  • Wong (1979). Schwartz spaces, nuclear spaces, and tensor products. Berlin New York: Springer-Verlag. ISBN 3-540-09513-6. OCLC 5126158.CS1 maint: ref=harv (link)
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