Results of Semigroup of Linear Operators Generating a Regular Weak*-continuous Semigroup

Abstract

This paper present results of $\omega$-order preserving partial contraction mapping generating a regular weak*-continuous semigroup. We consider a semigroup on a Banach space $X$ and $B:X^\odot\rightarrow X^*$ is bounded, then the intertwining formula was used to define a semigroup $T^B(t)$ on $X^*$ which extends the perturbed semigroup $T^B_0(t)$ on $X^\odot$ using the variation of constants formula. We also investigated a certain class of weak*-continuous semigroups on dual space $X^*$ which contains both adjoint semigroups and their perturbations by operators $B:X^\odot\rightarrow X^*$.

Results of Semigroup of Linear Operators Generating a General Class of Semilinear Initial Value Problems

“…Omosowon et al [13], generated some analytic results of semigroup of linear operator with dynamic boundary conditions, and also in [11], Omosowon et al, introduced dual Properties of ω-order Reversing Partial Contraction Mapping in Semigroup of Linear Operator. Omosowon et al [10], established a regular weak*-continuous semigroup of linear operators, and also in [9], Omosowon et al, obtained a quasilinear equations of evolution on semigroup of linear operator.reversing partial contraction mapping generating a differential operator. Omosowon et al [12], deduced results of semigroup of linear equation generating a wave equation.…”

Results of semigroup of linear operators in extrapolation spaces

“…Neerven [8], presented some results on adjoint of semigroup of linear operators. Both in [9] and [10], Omosowon et al built a regular weak*-continuous semigroup of linear operators and presented quasilinear equations of evolution on the semigroup of linear operator, a differential operator is produced by partially contraction mapping in reverse.…”

Results of Semigroup of Linear Operator Generating a Quasilinear Equations of Evolution

“…Omosowon et al [10], proved some analytic results of semigroup of linear operator with dynamic boundary conditions, and also in [11], Omosowon et al, established dual Properties of ω-order Reversing Partial Contraction Mapping in Semigroup of Linear Operator. Omosowon et al [12], generated a regular weak*-continuous semigroup of linear operators. Pazy [13], introduced asymptotic behavior of the solution of an abstract evolution and some applications and also in [14], established a class of semi-linear equations of evolution.…”