An additivity formula for the strict global dimension of C(Ω)
Seytek Tabaldyev
Open Mathematics, Tome 12 (2014), p. 470-475 / Harvested from The Polish Digital Mathematics Library
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Let A be a unital strict Banach algebra, and let K + be the one-point compactification of a discrete topological space K. Denote by the weak tensor product of the algebra A and C(K +), the algebra of continuous functions on K +. We prove that if K has sufficiently large cardinality (depending on A), then the strict global dimension is equal to .

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:269153 
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     author = {Seytek Tabaldyev},
     title = {An additivity formula for the strict global dimension of C($\Omega$)},
     journal = {Open Mathematics},
     volume = {12},
     year = {2014},
     pages = {470-475},
     zbl = {1295.46057},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0350-5}
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Seytek Tabaldyev. An additivity formula for the strict global dimension of C(Ω). Open Mathematics, Tome 12 (2014) pp. 470-475. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0350-5/

[1] Grothendieck A., Produits Tensoriels Topologiques et Espaces Nucléaires, Mem. Amer. Math. Soc., 16, American Mathematical Society, Providence, 1955

[2] Helemskii A.Ya., The Homology of Banach and Topological Algebras, Math. Appl. (Soviet Ser.), 41, Kluwer, Dordrecht, 1989 http://dx.doi.org/10.1007/978-94-009-2354-6[Crossref]

[3] Khelemskiĭ; A.Ya., Smallest values assumed by the global homological dimension of Banach function algebras, Amer. Math. Soc. Transl., 1984, 124, 75–96

[4] Krichevets A.N., On homological dimension of C(Ω), VINITI preprint #9012-B86, 1986 (in Russian)

[5] Kurmakaeva E.Sh., Homological Properties of Algebras of Continuous Functions, PhD thesis, Moscow State University, 1991 (in Russian)

[6] Kurmakaeva E.Sh., Dependence of strict homological dimension of C(Ω) on the topology of Ω, Math. Notes, 1994, 55(3–4), 289–293 http://dx.doi.org/10.1007/BF02110783[Crossref]

[7] MacLane S., Homology, Grundlehren Math. Wiss., 114, Springer, Berlin, 1963

[8] Phillips R.S., On linear transformations, Trans. Amer. Math. Soc., 1940, 48(3), 516–541 http://dx.doi.org/10.1090/S0002-9947-1940-0004094-3[Crossref] | Zbl 0025.34202

[9] Selivanov Yu.V., The values assumed by the global dimension in certain classes of Banach algebras, Moscow Univ. Math. Bull., 1975, 30(1), 30–34 | Zbl 0307.46037

[10] Selivanov Yu.V., Homological dimensions of tensor products of Banach algebras, In: Banach Algebras’ 97, Blaubeuren, July 20–August 3, 1997, Walter de Gruyter, Berlin, 1998, 441–459 | Zbl 0915.46065

[11] Tabaldyev S.B., On strict homological dimensions of algebras of continuous functions, Math. Notes, 2006, 80(5–6), 715–725 http://dx.doi.org/10.1007/s11006-006-0192-6[Crossref] | Zbl 1130.46046

[12] Varopoulos N.Th., Some remarks on Q-algebras, Ann. Inst. Fourier (Grenoble), 1972, 22(4), 1–11 http://dx.doi.org/10.5802/aif.432[Crossref]