A Rearrangement Invariant Space Isometric to L P Coincides with L P
نویسندگان
چکیده
We precede the proof with some necessary definitions and notation. Two Banach lattices X and Y are said to be order isometric if there exists an isometry U of X onto Y which preserves the order, that is, U is an isometric surjective operator and U(x) ≥ 0 if and only if x ≥ 0. Let L0 = L0[0, 1] be the vector lattice of all (equivalence classes of) measurable real valued functions on [0, 1] and let μ denote Lebesgue measure. A Banach space E is called rearrangement invariant (r.i.) if the following three conditions hold:
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