The Gleason-Kahane-Zelazko theorem characterizes the continuous homomorphism of an associative, locally multiplicatively convex, sequentially complete algebra A into the field C among all linear forms on A. This chara...The Gleason-Kahane-Zelazko theorem characterizes the continuous homomorphism of an associative, locally multiplicatively convex, sequentially complete algebra A into the field C among all linear forms on A. This characterization will be applied along two different directions. In the case in which A is a commutative Banach algebra, the theorem yields the representation of some classes of continuous linear maps A: A → A as weighted composition operators, or as composition operators when A is a continuous algebra endomorphism. The theorem will then be applied to explore the behaviour of continuous linear forms on quasi-regular elements, when A is either the algebra of all Hilbert-Schmidt operators or a Hilbert algebra.展开更多
According to results established by DeLeeuw-Rudin-Wermer and by Forelli, all linear isometries of any Hardy space H p (p ? 1, p ≠ = 2) on the open unit disc Δ of ? are represented by weighted composition operators d...According to results established by DeLeeuw-Rudin-Wermer and by Forelli, all linear isometries of any Hardy space H p (p ? 1, p ≠ = 2) on the open unit disc Δ of ? are represented by weighted composition operators defined by inner functions on Δ. After reviewing (and completing when p = ∞) some of those results, the present report deals with a characterization of periodic and almost periodic semigroups of linear isometries of H p .展开更多
文摘The Gleason-Kahane-Zelazko theorem characterizes the continuous homomorphism of an associative, locally multiplicatively convex, sequentially complete algebra A into the field C among all linear forms on A. This characterization will be applied along two different directions. In the case in which A is a commutative Banach algebra, the theorem yields the representation of some classes of continuous linear maps A: A → A as weighted composition operators, or as composition operators when A is a continuous algebra endomorphism. The theorem will then be applied to explore the behaviour of continuous linear forms on quasi-regular elements, when A is either the algebra of all Hilbert-Schmidt operators or a Hilbert algebra.
文摘According to results established by DeLeeuw-Rudin-Wermer and by Forelli, all linear isometries of any Hardy space H p (p ? 1, p ≠ = 2) on the open unit disc Δ of ? are represented by weighted composition operators defined by inner functions on Δ. After reviewing (and completing when p = ∞) some of those results, the present report deals with a characterization of periodic and almost periodic semigroups of linear isometries of H p .
