A splitting theorem for subspaces and quotiens of D'

• Autorzy: Wengenroth, J.
• Języki publikacji: EN

Abstrakty

EN

We improve a recent splitting theorem of Domański and Vogt by showing that in the category of PLS-spaces each exact sequence 0 -> F -> X -> 0 splits whenever E is isomorphic to a subspace of D' and F is isomorphic to a quotient of D', the space of distributions on some open subse of [R^d].

Słowa kluczowe

PL

ciąg dokładny; funktor ekstensjonalny; rozkład

EN

exact sequence; Ext-functor; space of distributions; splitting

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2001
• Tom: Vol. 49, no 4
• Strony: 349--354
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Wengenroth, J.

• FB IV - Mathematik, Universitat Trier, D - 54286 Trier, Germany ,

Bibliografia

• [1] P. Domański, D. Vogt, A splitting theory for the space of distribution Studia Math., 140 (2000) 57-77.
• [2] P. Domański, D. Vogt, Distributional complexes split for positive dime sions, J. Reine Angew. Math., 522 (2000) 63-79.
• [3] L. Frerick, J. Wengenroth, A sufficient condition for vanishing of t derived projective limit functor, Arch. Math. (Basel), 67 (1996) 296-301.
• [4] P. J. Hilton, U. Stammbach, A course in homological algebra, 2nd ed., Springer, New York 1997.
• [5] V. P. Palamodov, Homological methods in the theory of locally cont spaces, Uspekhi Mat. Nauk, 26 (1971) 3-65 (in Russian); English transl.: Russian Mai Surveys, 26 (1971) 1-64.
• [6] M. Valdivia, Representaciones de los espacios D(Ω) y D'(Ω), Rev. Ri Acad. Cienc. Exact. Fis. Natur. Madrid, 72 (1978) 385-414.
• [7] D. Vogt, Sequence space representations of spaces of test functions and disc butions, in: Functional analysis, holornorphy, and approximation theory, ed.: G. I. Zapa Marcel Dekker, New York-Basel 1983,405-443.
• [8] D. Vogt, On the functors Ext1 (E, F) for Fréchet spaces, Studia Math., (1987) 163-197.
• [9] D. Vogt, Lectures on projective spectra of DF-spaces, AG Funktionalanalysis Düsseldorf-Wuppertal 1987.
• [10] D. Vogt Topics on projective spectra of (LB)-spaces, in: Advances in the theory of Fréchet spaces, ed.: T. Terzioĝlu, NATO Adv. Sci. Inst. Ser. C Math. Pl Sci., 287 (1989) 11-27.
• [11] J. Wengenroth, Acyclic inductive spectra of Prichet spaces, Studia Ma 120 (1996) 247-258.
• [12] N. Yoneda, On Ext and exact sequences, J. Fac. Sci. Univ. Tokyo Sect. (1960) 507-576.