Ordered locally convex spaces in which topological convergence and order convergence coincide
Article
Received:
- 20 Downloads
Keywords
Order Convergence Topological Convergence
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
Literature Cited
- 1.R. E. De Marr, “Order convergence in linear topological spaces,” Pacific J. Math.,14, 17–20 (1964).Google Scholar
- 2.B. Z. Vulikh and O. S. Korsakova, “On spaces in which norm-convergence coincides with order convergence,” Mat. Zametki,13, No. 2, 256–268 (1973).Google Scholar
- 3.B. Z. Vulikh and I. F. Danilenko, “On one method of partial ordering of a normed space,” Vestn. Leningradsk. Univ., Ser. Mat., Mekh., Astronom., No. 19, 18–22 (1970).Google Scholar
- 4.H. H. Schaefer, Topological Vector Spaces, Springer-Verlag (1971).Google Scholar
- 5.B. Z. Vulikh, Introduction to the Theory of Semi-Ordered Spaces [in Russian], Fizmatgiz, Moscow (1961).Google Scholar
- 6.I. I. Chuchaev, “On the generalization of the concept of solid and infrasolid cones,” Sib. Mat. Zh.,15, No. 3, 609–615 (1974).Google Scholar
- 7.I. I. Chuchaev, “Some examples of cones in normed spaces,” in: Thematic Collection [in Russian], No. 108, Mordovsk. Univ. (1974), pp. 24–30.Google Scholar
- 8.M. A. Krasnosel'skii, Positive Solutions of Operator Equations [in Russian], Fizmatgiz, Moscow (1962).Google Scholar
- 9.V. I. Azhorkin and I. A. Bakhtin, “On the geometry of cones of linear positive operators in a Banach space,” Trudy Tsentr. Zonal'nogo Ob″edineniya Matem. Kafedr., No. 11, 3–10 (1971).Google Scholar
- 10.I. I. Chuchaev, “On plasterable cones in locally convex spaces,” Vestn. Leningradsk. Univ., Ser. Mat., Mekh., Astronom., No. 7, 70–77 (1975).Google Scholar
- 11.A. L. Peressini, Ordered Topological Vector Spaces, Harper and Row, New York-London (1967).Google Scholar
- 12.E. A. Gurevich and G. Ya. Rotkovich, “Comparison of various definitions ofo-convergence in structures,” Uch. Zap. Leningradsk. Ped. Inst.,274, 52–58 (1965).Google Scholar
- 13.Y. Komura and S. Koshi, “Nuclear vector lattices,” Math. Ann.,163, 105–110 (1966).Google Scholar
- 14.I. Amemiya, “A generalization of Riesz-Fichers theorem,” J. Math. Soc. Japan,5, 353–354 (1953).Google Scholar
- 15.E. A. Lifshits, “Positively reproducing and positively normal operators,” Funktsional'. Analiz. Ego Prilozhen.,6, No. 1, 19–23 (1972).Google Scholar
- 16.H. E. Bohnenblust and S. Kakutani, “Concrete representations of (M)-spaces,” Ann. Math.,42, No. 2, 1025–1028 (1941).Google Scholar
- 17.Yu. A. Abramovich, “Certain theorems on normed structures,” Vestn. Leningradsk. Univ., Ser. Mat., Mekh., Astronom., No. 13, 5–11 (1971).Google Scholar
Copyright information
© Plenum Publishing Corporation 1977