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Small into-isomorphism from L∞ (A, μ) into L∞(B, υ)

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Abstract

In this paper we shall assert that if T is an isomorphism of L∞(Ω1, A, μ) into L∞(Ω2, B, υ) satisfying the condition ‖T‖·‖T −1‖⩽1+ɛ for ɛ∈\(\left( {0,\frac{1}{5}} \right)\), then\(\frac{T}{{\parallel T\parallel }}\) is close to an isometry with an error less than 6ε in some conditions.

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Authors and Affiliations

  1. Department of Mathematics, Nankai University, 300071, Tianjin, China

    Guanggui Ding

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  1. Guanggui Ding
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Correspondence to Guanggui Ding.

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Ding, G. Small into-isomorphism from L∞ (A, μ) into L∞(B, υ). Sci. China Ser. A-Math. 44, 273–279 (2001). https://doi.org/10.1007/BF02878706

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  • DOI: https://doi.org/10.1007/BF02878706

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