The Interpolative Ideal of Bloch Mappings
Inspired by the interpolative ideal procedure for linear operators due to Matter, the concept of interpolative ideals of a Banach normalized Bloch ideal IB∧ is introduced. For σ∈0,1, we prove that the generated ideal IB∧σ is an injective Banach normalized Bloch ideal which is located between the inj...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2025-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/jofs/6987953 |
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| Summary: | Inspired by the interpolative ideal procedure for linear operators due to Matter, the concept of interpolative ideals of a Banach normalized Bloch ideal IB∧ is introduced. For σ∈0,1, we prove that the generated ideal IB∧σ is an injective Banach normalized Bloch ideal which is located between the injective hull and the closed injective hull of IB∧. We apply this interpolative procedure to normalized Bloch ideals generated by composition and duality. In particular, normalized Bloch ideals generated by composition with p-summing operator ideals are characterized in terms of a Pietsch-type domination property and a summability property. |
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| ISSN: | 2314-8888 |