It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend...It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend and improve the corresponding results of previous literature.展开更多
That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and...That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and that a compact inverse semigroup is topologically isomorphic to a strict projective limit of compact metric inverse semigroups are proved. It is also demonstrated that Hom (S,T) is a topological inverse semigroup provided that S or T is a topological inverse semigroup with some other conditions. Being proved by means of the combination of topological semigroup theory with inverse semigroup theory, all these results generalize the corresponding ones related to topological semigroups or topological groups.展开更多
基金Project of Sichuan Provincial Science and Technology Department (No.2007J13-006)
文摘It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend and improve the corresponding results of previous literature.
文摘That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and that a compact inverse semigroup is topologically isomorphic to a strict projective limit of compact metric inverse semigroups are proved. It is also demonstrated that Hom (S,T) is a topological inverse semigroup provided that S or T is a topological inverse semigroup with some other conditions. Being proved by means of the combination of topological semigroup theory with inverse semigroup theory, all these results generalize the corresponding ones related to topological semigroups or topological groups.
