Extension of contractive projections

2024/12/19 by Fu, Xiangdi, Guo, Kunyu, Li, Dilong
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2412.14808

Abstract

Through the establishment of several extension theorems, we provide explicit expressions for all contractive projections and 1-complemented subspaces in the Hardy space H^p(\mathbbT) for 1≤ p<∞, p≠ 2. Our characterization leads to two corollaries: first, all nontrivial 1-complemented subspaces of H^p(\mathbbT) are isometric to H^p(\mathbbT); second, all contractive projections on H^p(\mathbbT) are restrictions of contractive projections on L^p(\mathbbT) that leave H^p(\mathbbT) invariant. The first corollary provides examples of prime Banach spaces in the isometric sense, while the second answers a question posed by P. Wojtaszczyk in 2003.

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