A Note on Reflexivity |
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Authors: | Hassan Yousefi |
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Affiliation: | Department of Mathematics, Weber State University, Ogden, UT, USA |
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Abstract: | We prove some new results on Hadwin's general version of reflexivity that reduce the study of E-reflexivity (or E-hyperreflexivity) of a linear subspace to a smaller linear subspace. By applying our abstract results, we present a simple proof of D. Hadwin's theorem, which states that every C∗-algebra is approximately hyperreflexive. We also prove that the image of any C∗-algebra under any bounded unital homomorphism into the operators on a Banach space is approximately reflexive. We introduce a new version of reflexivity, called approximate algebraic reflexivity, and study its properties. |
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Keywords: | Reflexivity Algebraic reflexivity Approximate reflexivity Hyperreflexivity |
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