Antiproximinal ѕets in Banach ѕpaces
S. Cobzaş (1999)
Acta Universitatis Carolinae. Mathematica et Physica
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Displaying similar documents to “Some open problems on best approximation in normed linear spaces”
Antiproximinal ѕets in Banach ѕpaces
Geometric properties of Banach spaces and the existence of nearest and farthest points.
Cobzaş, Stefan (2005)
Abstract and Applied Analysis
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Remarks on separation of convex sets, fixed-point theorem, and applications in theory of linear operators.
Soltanov, Kamal N. (2007)
Fixed Point Theory and Applications [electronic only]
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On norm-attaining functionals
Maria D. Acosta, Vicente Montesinos (2006)
Acta Universitatis Carolinae. Mathematica et Physica
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Complex Banach spaces with Valdivia dual unit ball.
Ondrej F. K. Kalenda (2005)
Extracta Mathematicae
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We study the classes of complex Banach spaces with Valdivia dual unit ball. We give complex analogues of several theorems on real spaces. Further we study relationship of these complex Banach spaces with their real versions and that of real Banach spaces and their complexification. We also formulate several open problems.
A class of spaces lacking normal structure
W. L. Bynum (1972)
Compositio Mathematica
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Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces
P. Holický, O. F. K. Kalenda, L. Veselý, L. Zajíček (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction also gives a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals. ...