STABILITY OF ε-ISOMETRIES ON L∞-SPACES

doi:10.1007/s10473-019-0619-2

Abstract

Abstract: In this article, we discuss the stability of ε-isometries for L_∞,λ-spaces. Indeed, we first study the relationship among separably injectivity, injectivity, cardinality injectivity and universally left stability of L_∞,λ-spaces as well as we show that the second duals of universally left-stable spaces are injective, which gives a partial answer to a question of Bao-Cheng-Cheng-Dai, and then we prove a sharpen quantitative and generalized Sobczyk theorem which gives examples of nonseparable L_∞-spaces X (but not injective) such that the couple (X, Y) is stable for every separable space Y. This gives a new positive answer to Qian's problem.

Key words: stability, ε-isometry, L_∞-space

CLC Number:

46B04

Duanxu DAI. STABILITY OF ε-ISOMETRIES ON L_∞-SPACES[J].Acta mathematica scientia,Series B, 2019, 39(6): 1733-1742.

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STABILITY OF ε-ISOMETRIES ON L_∞-SPACES

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