Bi-parameter Semigroups of linear operators
نویسندگان
چکیده
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 , whose first and second generators are d and σ, respectively, and if d is also a σ-derivation then dn(ab) = (d + σ)n(a) (d + σ)n(b) and αt,0(ab) = αt,1(a) αt,1(b) for all a, b ∈ X . c © Electronic Journal of Theoretical Physics. All rights reserved.
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