From Wikipedia, the free encyclopedia
Mathematics concept
In
mathematics, particularly in
functional analysis, a Mackey space is a
locally convex topological vector space X such that the
topology of X coincides with the
Mackey topology τ(X,X′), the
finest topology which still preserves the
continuous dual. They are named after
George Mackey.
Examples
Examples of locally convex spaces that are Mackey spaces include:
Properties
- A locally convex space
with continuous dual
is a Mackey space if and only if each convex and
-relatively compact subset of
is equicontinuous.
- The
completion of a Mackey space is again a Mackey space.
[4]
- A separated quotient of a Mackey space is again a Mackey space.
- A Mackey space need not be
separable,
complete,
quasi-barrelled, nor
-quasi-barrelled.
See also
References
-
^ Schaefer (1999) p. 138
-
^ Schaefer (1999) p. 133
-
Bourbaki, Nicolas (1987) [1981]. Topological Vector Spaces: Chapters 1–5.
Éléments de mathématique. Translated by Eggleston, H.G.; Madan, S. Berlin New York: Springer-Verlag.
ISBN
3-540-13627-4.
OCLC
17499190.
-
Grothendieck, Alexander (1973).
Topological Vector Spaces. Translated by Chaljub, Orlando. New York: Gordon and Breach Science Publishers.
ISBN
978-0-677-30020-7.
OCLC
886098.
- Khaleelulla, S. M. (1982). Counterexamples in Topological Vector Spaces.
Lecture Notes in Mathematics. Vol. 936. Berlin, Heidelberg, New York:
Springer-Verlag.
ISBN
978-3-540-11565-6.
OCLC
8588370.
- Robertson, A.P.; W.J. Robertson (1964). Topological vector spaces. Cambridge Tracts in Mathematics. Vol. 53.
Cambridge University Press. p. 81.
-
Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces.
GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. pp. 132–133.
ISBN
978-1-4612-7155-0.
OCLC
840278135.
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