### Abstract

Let (i, H, E) and (j, K, F) be abstract Wiener spaces and let α be a reasonable norm on E ⊗ F. We are interested in the following problem: is (i ⊗ j, H \ ̂bo_{2} K, E \ ̂bo_{αF}) an abstract Wiener space ? The first thing we do is to prove that the setting of the problem is meaningfull: namely, i ⊗ j is always a continuous one to one map from H \ ̂bo_{2} K into E \ ̂bo_{α}F. Then we exhibit an example which shows that the answer cannot be positive in full generality. Finally we prove that if F=L^{p}(X,X,λ) for some σ-finite measure λ ≥ 0 then (i⊗j, H⊗_{2}K,L^{p}(X,X,λ) is an abstract Wiener space. By-products are some new results on γ-radonifying operators, and new examples of Banach spaces and cross norms for which the answer is affirmative (in particular α = π the projective norm, and F=L^{1}(X,X,λ)).

Original language | English (US) |
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Pages (from-to) | 297-310 |

Number of pages | 14 |

Journal | Journal of Functional Analysis |

Volume | 33 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1979 |

### All Science Journal Classification (ASJC) codes

- Analysis

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## Cite this

^{p}(E).

*Journal of Functional Analysis*,

*33*(3), 297-310. https://doi.org/10.1016/0022-1236(79)90069-7