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We prove that a Banach space that is convex-transitive
and such that for some element u in the unit sphere, and for every
subspace M containing u, it happens that the subset of norm attaining
functionals on M is second Baire category in M∗ is, in fact,
almost-transitive and superreflexive. We also obtain a characterization
of finite-dimensional spaces in terms of functions that attain
their supremum: a Banach space is finite-dimensional if, for every
equivalent norm, every rank-one operator attains its numerical radius.
Finally, we describe the subset of norm attaining functionals
on a space isomorphic to 1, where the norm is the restriction of
a Luxembourg norm on L1. In fact, the subset of norm attaining
functionals for this norm coincides with the subset of norm attaining
functionals for the usual norm.
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참고문헌 (23)
참고문헌 신청
/ / Numerical Ranges of Operators on Normed Spacesand of Elements of Normed Algebras
/ 1964 / Weak compactness and reexivity 2
/ 1966 / On nonseparable reexive Banach spaces 72
/ 1974 / Some properties of the set of functionals thatattain a supremum on the unit sphere 26
/ 1975 / The existence in every separable Banach spaceof a fundamental total and bounded biorthogonal sequence and related construc-tions of uniformly bounded orthogonal sys
/ 1964 / Weak compactness and reexivity 2
/ 1966 / On nonseparable reexive Banach spaces 72
/ 1974 / Some properties of the set of functionals thatattain a supremum on the unit sphere 26
/ 1975 / The existence in every separable Banach spaceof a fundamental total and bounded biorthogonal sequence and related construc-tions of uniformly bounded orthogonal sys
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