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Range transformations
on a Banach function algebra. II
Osamu Hatori |
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Vol. 138 (1989), No. 1, 89–118
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Abstract |
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In this paper, localization for ultraseparability is introduced and a local version of Bernard’s lemma is proven. By using these results it is shown that a function in Op(ID,Re A) is harmonic near the origin for a uniformly closed subalgebra A of C0(Y ) and an ideal I of A unless the uniform closure cl I of I is self-adjoint; in particular, it is shown that cl I is self-adjoint if Re I ⋅ Re I ⊂ Re A, which is not true when I is merely a closed subalgebra of A. |
Mathematical Subject Classification 2000
Primary: 46J10
Secondary: 46H30
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Milestones
Received: 25 October 1987
Revised: 24 March 1988
Published: 1 May 1989
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Authors |
| Osamu Hatori | |
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