The noncommutative Hardy spaces
H∞(α) and
H1(α) are introduced with respect to a σ-weakly continuous flow α={α
t} of *-automorphisms of a von Neumann algebra. In case that the algebra is α-finite the algebra
H∞(α) becomes a maximal subdiagonal algebra. The concept of
C*-subdiagonal algebras will also be given for
C*-algebras as a noncommutative counterpart of the algebras of generalized analytic functions. Examples of maximal
C*-subdiagonal algebras and their structures are discussed.
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