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Danes’ Drop Theorem in locally convex spaces. (English) Zbl 0863.46003

Summary: Danes’ Drop Theorem is generalized to locally convex spaces.

MSC:

46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
46B20 Geometry and structure of normed linear spaces
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References:

[1] Josef Daneš, A geometric theorem useful in nonlinear functional analysis, Boll. Un. Mat. Ital. (4) 6 (1972), 369 – 375 (English, with Italian summary). · Zbl 0236.47053
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[9] M. Turcini, Mapping theorems via variable drops in Banach spaces, Rend. Istit. Lombardo, Sci. A 114 (1980), 164-168.
[10] J. R. Giles, Brailey Sims, and A. C. Yorke, On the drop and weak drop properties for a Banach space, Bull. Austral. Math. Soc. 41 (1990), no. 3, 503 – 507. · Zbl 0692.46007 · doi:10.1017/S0004972700018384
[11] Denka N. Kutzarova, On drop property of convex sets in Banach spaces, Constructive Theory of Functions’ 87, Sofia (1988), 283-287. · Zbl 0721.41048
[12] D. N. Kutzarova and S. Rolewicz, On nearly uniformly convex sets, Arch. Math. (Basel) 57 (1991), no. 4, 385 – 394. · Zbl 0756.52004 · doi:10.1007/BF01198964
[13] Robert R. Phelps, Convex functions, monotone operators and differentiability, Lecture Notes in Mathematics, vol. 1364, Springer-Verlag, Berlin, 1989. · Zbl 0658.46035
[14] John R. Giles, Convex analysis with application in the differentiation of convex functions, Research Notes in Mathematics, vol. 58, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. · Zbl 0486.46001
[15] P. Georgiev, D. Kutzarova and A. Maaden, On the smooth drop property, Nonlinear Anal. 26 (1996), 595-602. CMP 96:03 · Zbl 0872.46010
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