p-Summing Bloch mappings on the complex unit disc
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URI: http://hdl.handle.net/10835/15644
ISSN: 2662-2033
ISSN: 1735-8787
DOI: 10.1007/s43037-023-00318-6
ISSN: 2662-2033
ISSN: 1735-8787
DOI: 10.1007/s43037-023-00318-6
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2024-01-22Resumen
The notion of p-summing Bloch mapping from the complex unit open disc D into a complex Banach space X is introduced for any 1 ≤ p ≤ ∞. It is shown that the linear space of such mappings, equipped with a natural seminorm πpB , is Möbius invariant. Moreover, its subspace consisting of all those mappings which preserve the zero is an injective Banach ideal of normalized Bloch mappings. Bloch versions of the Pietsch’s domination/factorization Theorem and the Maurey’s extrapolation Theorem are presented. We also introduce the spaces of X-valued Bloch molecules on D and identify the spaces of normalized p-summing Bloch mappings from D into X∗ under the norm πpB with the duals of such spaces of molecules under the Bloch version of the p∗-Chevet–Saphar tensor norms dp∗ .
Palabra/s clave
Vector-valued Bloch mapping
Compact Bloch mapping
Banach-valued Bloch molecule
Bloch-free Banach space