Infrabarreled space
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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
- Every quasi-complete infrabarreled space is barreled.[1]
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
- ↑ 1.0 1.1 1.2 Schaefer 1999, p. 142.
- ↑ 2.0 2.1 2.2 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.
- Trèves, François (August 6, 2006). Topological Vector Spaces, Distributions and Kernels. Mineola, N.Y.: Dover Publications. ISBN 978-0-486-45352-1. OCLC 853623322.
- Wong (1979). Schwartz spaces, nuclear spaces, and tensor products. Berlin New York: Springer-Verlag. ISBN 3-540-09513-6. OCLC 5126158.
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