Contraction Quasi Semigroups and Their Applications in Decomposing Hilbert Spaces

This paper addresses the problem of implementations of a strongly continuous quasi semigroup in analyzing non-autonomous Cauchy problems induced by dissipative operators. The implementations are closely related to contraction quasi semigroups. Lumer-Phillips Theorem for the contraction quasi semigroups is proved. Relationships between the contraction quasi semigroups and their cogenerator are also explored. Furthermore, we show that the contraction quasi semigroups are applicable in decomposing Hilbert spaces.