| Title:
|
Products and projective limits of function spaces (English) |
| Author:
|
Kačena, Miroslav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
547-578 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce a notion of a product and projective limit of function spaces. We show that the Choquet boundary of the product space is the product of Choquet boundaries. Next we show that the product of simplicial spaces is simplicial. We also show that the maximal measures on the product space are exactly those with maximal projections. We show similar characterizations of the Choquet boundary and the space of maximal measures for the projective limit of function spaces under some additional assumptions and we prove that the projective limit of simplicial spaces is simplicial. (English) |
| Keyword:
|
Choquet theory |
| Keyword:
|
function space |
| Keyword:
|
product |
| Keyword:
|
projective limit |
| Keyword:
|
simplicial space |
| MSC:
|
26B25 |
| MSC:
|
46A13 |
| MSC:
|
46A32 |
| MSC:
|
46A55 |
| MSC:
|
46E15 |
| MSC:
|
46M40 |
| idZBL:
|
Zbl 1212.46016 |
| idMR:
|
MR2493938 |
| . |
| Date available:
|
2009-05-05T17:13:11Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119746 |
| . |
| Reference:
|
[1] Alfsen E.M.: Compact Convex Sets and Boundary Integrals.Springer, New York-Heidelberg, 1971. Zbl 0209.42601, MR 0445271 |
| Reference:
|
[2] Batty C.J.K.: Maximal measures on tensor products of compact convex sets.Quart. J. Math. Oxford Ser. (2) 33 (1982), 1-10. Zbl 0439.46008, MR 0689847, 10.1093/qmath/33.1.1 |
| Reference:
|
[3] Behrends E., Wittstock G.: Tensorprodukte kompakter konvexer Mengen.Invent. Math. 10 (1970), 251-266. Zbl 0197.38406, MR 0272693, 10.1007/BF01403252 |
| Reference:
|
[4] Boboc N., Cornea A.: Convex cones of lower semicontinuous functions on compact spaces.Rev. Roumaine Math. Pures Appl. 12 (1967), 471-525. Zbl 0155.17301, MR 0216278 |
| Reference:
|
[5] Bourbaki N.: General Topology. Chapters 1-4.2nd printing, Springer, Berlin, 1989. Zbl 1107.54001, MR 0979294 |
| Reference:
|
[6] Davies E.B., Vincent-Smith G.F.: Tensor products, infinite products, and projective limits of Choquet simplexes.Math. Scand. 22 (1968), 145-164. Zbl 0176.42802, MR 0243316 |
| Reference:
|
[7] Enflo P.: A counterexample to the approximation problem in Banach spaces.Acta Math. 130 (1973), 309-317. Zbl 0267.46012, MR 0402468, 10.1007/BF02392270 |
| Reference:
|
[8] Fremlin D.H.: Measure Theory, vol. 4.Torres Fremlin, 2003. Zbl 1166.28001, MR 2462372 |
| Reference:
|
[9] Grossman M.W.: A Choquet boundary for the product of two compact spaces.Proc. Amer. Math. Soc. 16 (1965), 967-971. Zbl 0139.06702, MR 0180879, 10.1090/S0002-9939-1965-0180879-0 |
| Reference:
|
[10] Grossman M.W.: Limits and colimits in certain categories of spaces of continuous functions.Dissertationes Math. 79 (1970). Zbl 0221.46062, MR 0276740 |
| Reference:
|
[11] Hulanicki A., Phelps R.R.: Some applications of tensor products of partially-ordered linear spaces.J. Funct. Anal. 2 (1968), 177-201. Zbl 0159.41504, MR 0225135, 10.1016/0022-1236(68)90016-5 |
| Reference:
|
[12] Jacobs K.: Measure and Integral.Academic Press, New York-London, 1978. Zbl 0446.28001, MR 0514702 |
| Reference:
|
[13] Jellett F.: Homomorphisms and inverse limits of Choquet simplexes.Math. Z. 103 (1968), 219-226. Zbl 0164.43303, MR 0221278, 10.1007/BF01111040 |
| Reference:
|
[14] Johnson W.B., Lindenstrauss J. (Eds.): Handbook of the Geometry of Banach Spaces.Volume 1, North-Holland, Amsterdam, 2001. Zbl 1013.46001, MR 1863689 |
| Reference:
|
[15] Kačena M., Spurný J.: Affine images of compact convex sets and maximal measures.preprint, available at http://www.karlin.mff.cuni.cz/kma-preprints. |
| Reference:
|
[16] Lazar A.J.: Affine products of simplexes.Math. Scand. 22 (1968), 165-175. Zbl 0176.42803, MR 0251500 |
| Reference:
|
[17] Lazar A.J.: Spaces of affine continuous functions on simplexes.Trans. Amer. Math. Soc. 134 (1968), 503-525. Zbl 0174.17102, MR 0233188, 10.1090/S0002-9947-1968-0233188-2 |
| Reference:
|
[18] Namioka I., Phelps R.R.: Tensor products of compact convex sets.Pacific J. Math. 31 (1969), 469-480. MR 0271689, 10.2140/pjm.1969.31.469 |
| Reference:
|
[19] Semadeni Z.: Banach spaces of continuous functions. Vol. I..Monografie Matematyczne, Tom 55, PWN-Polish Scientific Publishers, Warszawa, 1971. MR 0296671 |
| . |
