Electronic Journal of Theoretical Physics, Volume (9), No (26), Year (2012-1) , Pages (173-182)

Title : ( Bi-parameter Semigroups of linear operators )

Authors: Shirin Hejazian , hussein mahdavian rad , Madjid Mirzavaziri , Hossein Mohammadian ,

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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,s0 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.


, One Parameter Semigroup, Bi-parameter Semigroup, σ-derivation, Infinitesimal
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author = {Hejazian, Shirin and Mahdavian Rad, Hussein and Mirzavaziri, Madjid and Mohammadian, Hossein},
title = {Bi-parameter Semigroups of linear operators},
journal = {Electronic Journal of Theoretical Physics},
year = {2012},
volume = {9},
number = {26},
month = {January},
issn = {1729-5254},
pages = {173--182},
numpages = {9},
keywords = {One Parameter Semigroup; Bi-parameter Semigroup; σ-derivation; Infinitesimal generator},


%0 Journal Article
%T Bi-parameter Semigroups of linear operators
%A Hejazian, Shirin
%A Mahdavian Rad, Hussein
%A Mirzavaziri, Madjid
%A Mohammadian, Hossein
%J Electronic Journal of Theoretical Physics
%@ 1729-5254
%D 2012