Geodesic
Grothendieck theorem for some uniform algebras and modules over them
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 47, Tome 480 (2019), pp. 108-121 Cet article a éte moissonné depuis la source Math-Net.Ru

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Under certain additional assumptions, it is proved that a $w^*$-closed subalgebra $X$ of $L^\infty(\mu)$ (more generally, a $w^*$-closed module over $X$) verifies the Grothendieck theorem. The assumptions in question imitate a property of the classical harmonic conjugation operator but are less binding than it is usual in similar settings. Specifically, $\mu$ may fail to be multiplicative on $X$, etc. 
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I. K. Zlotnikov; S. V. Kislyakov. Grothendieck theorem for some uniform algebras and modules over them. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 47, Tome 480 (2019), pp. 108-121. http://geodesic.mathdoc.fr/item/ZNSL_2019_480_a7/

[1] S. V. Kislyakov, “Absolyutno summiruyuschie operatory na disk-algebre”, Algebra i analiz, 3:4, 1–77 | MR

[2] J. Lindenstrauss, A. Pełczyński, “Absolutely summing operators in $L_p$-spaces and their applications”, Studia Math., 29 (1968), 275–326 | DOI | MR | Zbl

[3] J. Bourgain, “New-Banach space properties of the disc algebra and $H^\infty$”, Acta Math., 152 (1984), 1–46 | DOI | MR

[4] F. Lancien, Géométrie des espaces de Banach dans certains espaces de Hardy abstraits, Thèse de doctorat en mathématiques, Université Paris 6, 1993 | Zbl

[5] F. Lancien, “Generalization of Bourgain's theorem about $L^1/H^1$ for weak*-Dirichlet algebras”, Houston J. Math., 20:1 (1994), 47–61 | MR | Zbl

[6] S. V. Kislyakov, I. K. Zlotnikov, “Interpolation for intersections of Hardy-type spaces”, Israel J. Math. (to appear)

[7] W. B. Johnson, J. Lindenstrauss, “Basic concepts in the geometry of Banach spaces”, Handbook of the geometry of Banach spaces, v. 1, Elsevier, 2001, 1–84 | MR | Zbl