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RESEARCH PRODUCT

Restricted Uniform Boundedness in Banach Spaces

Olav NygaardMärt P Ldvere

subject

Discrete mathematicsMathematics (miscellaneous)Bounded setUniform boundedness principleBounded functionBanach spaceUniform boundednessFinite-rank operatorBounded inverse theoremBounded operatorMathematics

description

Precise conditions for a subset A of a Banach space X are known in order that pointwise bounded on A sequences of bounded linear functionals on X are uniformly bounded. In this paper, we study such conditions under the extra assumption that the functionals belong to a given linear subspace &#915 of X *. When &#915 = X *, these conditions are known to be the same ones assuring a bounded linear operator into X , having A in its image, to be onto. We prove that, for A , deciding uniform boundedness of sequences in &#915 is the same property as deciding surjectivity for certain classes of operators. Keywords: Uniform boundedness; thick set; boundedness deciding set Quaestiones Mathematicae 32(2009), 5–14

yearjournalcountryeditionlanguage
2009-03-01Quaestiones Mathematicae
https://doi.org/10.2989/qm.2009.32.1.2.704