Book Review: One-parameter semigroups of positive operators
نویسندگان
چکیده
منابع مشابه
Bi-parameter Semigroups of linear operators
Abstract: Let X be a Banach space. We define the concept of a bi-parameter semigroup on X and its first and second generators. We also study bi-parameter semigroups on Banach algebras. A relation between uniformly continuous bi-parameter semigroups and σ-derivations is also established. It is proved that if {αt,s}t,s 0 is a uniformly continuous bi-parameter semigroup on a Banach algebra X , who...
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We give an overview of the F–product construction and the corresponding nonstandard constructions and show that (in the case of bounded ultrapowers) both constructs are isomorphic (theorem 3.15). From this we also follow a little “classical” corollary (3.14). The nonstandard construction has been investigated in [Wol84] and [Wol], the corresponding classical constructions first appeared in [Der...
متن کاملStability of Individual Elements under One-parameter Semigroups
Let {r(Z):Z>0} be a C0-semigroup on a Banach space X with generator A , and let x € X. If a (A) n ;'R is empty and t »-> T(t)x is uniformly continuous, then ||7"(Z)jc|| —> 0 as t —» oo . If the semigroup is sun-reflexive, o(A)CiiR is countable, Pa(A)DiS. is empty, and 1 >-> T(t)x is uniformly weakly continuous, then T(t)x —► 0 weakly as t —» oo . Questions of almost periodicity and of stabiliza...
متن کاملMultiplier Algebras, Banach Bundles, and One-parameter Semigroups
Several results are proved concerning representations of multiplier algebras that arise as extensions of representations of underlying Banach algebras. These results are then used to rederive Kisyński’s generalisation of the Hille–Yosida theorem and to establish two generalisations of the Trotter–Kato theorem, one of which, involving Banach bundles, is abstract and the other is classical in cha...
متن کاملSemigroups of Linear Operators
Our goal is to define exponentials of linear operators. We will try to construct etA as a linear operator, where A : D(A)→ X is a general linear operator, not necessarily bounded. Notationally, it seems like we are looking for a solution to μ̇(t) = Aμ(t), μ(0) = μ0, and we would like to write μ(t) = eμ0. It turns out that this will hold once we make sense of the terms. How can we construct etA w...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1987
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1987-15597-2