Analyse Fonctionnelle Espace de Hilbert d'opérateurs et Interpolation complexe par Gilles Pisier Note présentée par Alain Connes Résumé. Soit H un espace hilbertien de dimension infinie. On montre qu'il existe un sous-espace fermé de B(H) qui est hilbertien etcompì etement isométriquè a son antidual au sens de la théorie des espaces d'opérateurs dévelopée récemment par Blecher-Paulsen et Effros...

This paper investigates the distribution and nonuniform complexity of problems that are com plete or weakly complete for ESPACE under nonuniform reductions that are computed by polynomial size circuits P Poly Turing reductions and P Poly many one reductions A tight exponential lower bound on the space bounded Kolmogorov complexities of weakly P Poly Turing complete problems is established A Sma...

Every language that is P m -hard for ESPACE is shown to have unusually small complexity cores and unusually low space-bounded Kolmogorov complexity. It follows that the Pm-complete languages form a measure 0 subset of ESPACE.

This paper investigates the structure of ESPACE under nonuniformTuring reductions that are computed by polynomial size circuits P Poly Turing reductions A Small Span Theorem is proven for such reductions This result says that every language A in ESPACE satis es at least one of the following two conditions i The lower P Poly Turing span of A consisting of all languages that are P Poly Turing red...

It is shown that almost every language in ESPACE is very hard to approximate with circuits It follows that P BPP implies that E is a measure subset of ESPACE