New sufficient conditions for the law of the iterated logarithm in Banach spaces

Michel Weber

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S. CHEVET, p-ellipsoïdes de $l^{2}$ . Mesures cylindriques gaussiennes 439-441 W. WOJTYŃSKI On conditional bases in non-nuclear Fréchet spaces 441 C. BESSAGA, A theorem on complemented subspaces of nuclear spaces 441-442 C. MCCARTHY, Optimal conditioning of operators 442-443 D. PRZEWORSKA-ROLEWICZ, On algebraic derivative 443-444 N. TOMCZAK, A remark (p,q)-absolutely summing operators in $L_{p}$ -spaces 444-445 W. MLAK, Decompositions of operator representations of function algebras 445-446 A. PERSSON,...

Spaces of type $H^{\infty} + C$

Walter Rudin (1975)

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A simple theorem is proved which states a sufficient condition for the sum ot two closed subspaces of a Banach space to be closed. This leads to several analogues of Sarason’s theorem which states that $H^{\infty} + C$ is a closed subalgebra of $L^{\infty}$ . In these analogues, the unit circle is replaces by other groups, and the unit disc is replaced by polydiscs or by balls in spaces of several complex variables. Sums of closed ideals in Banach algebras are also studied.