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A complex interpolation formula for tensor products of vector-valued Banach function spaces

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Abstract.

We prove the complex interpolation formula \([{X_0}{(E_0)} \tilde{\otimes} _{\varepsilon} {Y_0}{(F_0)}, {X_1}{(E_1)} \tilde {\otimes} _{\varepsilon } {Y_1}{(F_1)}]_\theta = [{X_0}{(E_0)},{X_1}{(E_1)}]_\theta \tilde {\otimes} _{\varepsilon } [{Y_0}{(F_0)},{Y_1}{(F_1)}]_\theta , \)for the injective tensor product of vector-valued Banach function spaces X i (E i ) and Y i (F i ) satisfying certain geometric assumptions. This result unifies results of Kouba, and moreover, our approach offers an alternate proof of Kouba's interpolation formula for scalar-valued Banach function spaces.

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  1. Fachbereich Mathematik, Carl von Ossietzky Universität Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany, , , , , , DE

    Andreas Defant & Carsten Michels

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  1. Andreas Defant
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  2. Carsten Michels
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Received: 22.1.1999

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Defant, A., Michels, C. A complex interpolation formula for tensor products of vector-valued Banach function spaces. Arch. Math. 74, 441–451 (2000). https://doi.org/10.1007/PL00000425

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  • DOI: https://doi.org/10.1007/PL00000425

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