Levi forms, differential forms of type (0,1) and pseudoconvexity in Banach spaces
Ewa Ligocka (1976)
Annales Polonici Mathematici
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Ewa Ligocka (1976)
Annales Polonici Mathematici
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Rafael Payá (1997)
Extracta Mathematicae
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The well known Bishop-Phelps Theorem asserts that the set of norm attaining linear forms on a Banach space is dense in the dual space [3]. This note is an outline of recent results by Y. S. Choi [5] and C. Finet and the author [7], which clarify the relation between two different ways of extending this theorem.
María D. Acosta (2006)
RACSAM
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The Bishop-Phelps Theorem states that the set of (bounded and linear) functionals on a Banach space that attain their norms is dense in the dual. In the complex case, Lomonosov proved that there may be a closed, convex and bounded subset C of a Banach space such that the set of functionals whose maximum modulus is attained on C is not dense in the dual. This paper contains a survey of versions for operators, multilinear forms and polynomials of the Bishop-Phelps Theorem. Lindenstrauss...
Saleh, Yousef (2008)
International Journal of Mathematics and Mathematical Sciences
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Saleh, Yousef (2000)
International Journal of Mathematics and Mathematical Sciences
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M. Jimenéz Sevilla, Rafael Payá (1998)
Studia Mathematica
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For each natural number N, we give an example of a Banach space X such that the set of norm attaining N-linear forms is dense in the space of all continuous N-linear forms on X, but there are continuous (N+1)-linear forms on X which cannot be approximated by norm attaining (N+1)-linear forms. Actually,X is the canonical predual of a suitable Lorentz sequence space. We also get the analogous result for homogeneous polynomials.
Maria Acosta (1998)
Studia Mathematica
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We show, for any Banach spaces X and Y, the denseness of the set of bilinear forms on X × Y whose third Arens transpose attains its norm. We also prove the denseness of the set of norm attaining multilinear mappings in the class of multilinear mappings which are weakly continuous on bounded sets, under some additional assumptions on the Banach spaces, and give several examples of classical spaces satisfying these hypotheses.
Andreas Čap (1990)
Commentationes Mathematicae Universitatis Carolinae
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