[Author]
 Oleg Reinov

[Title]
 $H^\infty$ and the Grothendieck approximation property

[AMS Subj-class]
 30H10 Hardy spaces
 46B28 Spaces of operators; tensor products; approximation properties

[Abstract]
 This is a version of a talk at the Workshop and Autumn School
 "Spaces of Analytic Functions and Singular Integrals (SAFSI2015)"
 Russia, St. Petersburg, October 12-15, 2015.

 We present a small survey of all (known to us, and we think to everybody)
 results, concerning the following open question: Does $H^\infty$ have the
 approximation property? Note that the best of the results is still the
 theorem, due to Bourgain-Reinov (1983): $H^\infty$ has the approximation
 property "up to log".

[Comments]
 LaTeX, English, 27 pp.

[Contact e-mail]
 orein51@mail.ru