On ‐null sequences and their relatives |
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Authors: | Kati Ain Eve Oja |
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Institution: | 1. Faculty of Mathematics and Computer Science, Tartu University, 50409 Tartu, Estonia;2. Estonian Academy of Sciences, 10130 Tallinn, Estonia |
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Abstract: | Let and , where is the conjugate index of p. We prove an omnibus theorem, which provides numerous equivalences for a sequence in a Banach space X to be a ‐null sequence. One of them is that is ‐null if and only if is null and relatively ‐compact. This equivalence is known in the “limit” case when , the case of the p‐null sequence and p‐compactness. Our approach is more direct and easier than those applied for the proof of the latter result. We apply it also to characterize the unconditional and weak versions of ‐null sequences. |
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Keywords: | Banach spaces ‐null sequences relatively ‐compact sets ‐compact operators operator ideals Primary: 46B50 Secondary: 46B20 46B45 47B07 47B10 47L20 |
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