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- W4360978951 abstract "Abstract Applying a linearization theorem due to Mujica (Trans Am Math Soc 324:867–887, 1991), we study the ideals of bounded holomorphic mappings $$mathcal {I}circ mathcal {H}^infty $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>I</mml:mi> <mml:mo>∘</mml:mo> <mml:msup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mi>∞</mml:mi> </mml:msup> </mml:mrow> </mml:math> generated by composition with an operator ideal $$mathcal {I}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>I</mml:mi> </mml:math> . The bounded-holomorphic dual ideal of $$mathcal {I}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>I</mml:mi> </mml:math> is introduced and its elements are characterized as those that admit a factorization through $$mathcal {I}^{textrm{dual}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mrow> <mml:mi>I</mml:mi> </mml:mrow> <mml:mtext>dual</mml:mtext> </mml:msup> </mml:math> . For complex Banach spaces E and F , we also analyze new ideals of bounded holomorphic mappings from an open subset $$Usubseteq E$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>U</mml:mi> <mml:mo>⊆</mml:mo> <mml:mi>E</mml:mi> </mml:mrow> </mml:math> to F such as p -integral holomorphic mappings and p -nuclear holomorphic mappings with $$1le p<infty $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>p</mml:mi> <mml:mo><</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> . We prove that every p -integral ( p -nuclear) holomorphic mapping from U to F has relatively weakly compact (compact) range." @default.
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- W4360978951 date "2023-03-19" @default.
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- W4360978951 title "On Composition Ideals and Dual Ideals of Bounded Holomorphic Mappings" @default.
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- W4360978951 doi "https://doi.org/10.1007/s00025-023-01868-9" @default.
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