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

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In this paper we shall assert that if T is an isomorphism ofL∞(Ω1,A,μ) into L∞(Ω2,B,ν) satisfying the condition ‖T‖·‖T-1‖≤1+ε for ε∈ is close to an isometry with an error less than 6ε in some conditions.
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