“Smith space”的意思、由来-开放百科全书

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Smith space

释义

See also
Notes
References

In functional analysis and related areas of mathematics, Smith space is a complete compactly generated locally convex space having a compact set which absorbs every other compact set (i.e. for some ).

Smith spaces are named after

[https://www.genealogy.math.ndsu.nodak.edu/id.php?id=4032 Marianne Ruth Freundlich Smith], who introduced them{{sfn|Smith|1952}} as duals to Banach spaces in some versions of duality theory for topological vector spaces. All Smith spaces are stereotype and are in the stereotype duality relations with Banach spaces:{{sfn|Akbarov|2003|p=220}}{{sfn|Akbarov|2009|p=467}}

for any Banach space its stereotype dual space^[1] is a Smith space,

and vice versa, for any Smith space its stereotype dual space is a Banach space.

Notes

1. ^The stereotype dual space to a locally convex space

is the space

of all linear continuous functionals

endowed with the topology of uniform convergence on totally bounded sets in

References

{{cite journal|last=Smith|first=M.F.|title=The Pontrjagin duality theorem in linear spaces|journal=Annals of Mathematics|year=1952|volume=56|issue=2|pages=248–253|doi=10.2307/1969798|jstor=1969798| ref = harv}}
{{cite journal|last=Akbarov|first=S.S.|title=Pontryagin duality in the theory of topological vector spaces and in topological algebra|journal=Journal of Mathematical Sciences|year=2003|volume=113|issue=2|pages=179–349|doi=10.1023/A:1020929201133|url=http://www.springerlink.com/content/k62m72960101g6q2/| ref = harv}}
{{cite journal|last=Akbarov|first=S.S.|title=Holomorphic functions of exponential type and duality for Stein groups with algebraic connected component of identity|journal=Journal of Mathematical Sciences|year=2009|volume=162|issue=4|pages=459–586|doi=10.1007/s10958-009-9646-1|subscription=yes|url=http://www.springerlink.com/content/u07317731010573l/| ref = harv|arxiv=0806.3205}}
{{cite thesis |type=PhD |last=Furber |first=R.W.J. |date=2017 |title=Categorical Duality in Probability and Quantum Foundations|publisher=Radboud University| ref = harv}}

1 : Functional analysis

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See also

Notes

References