| Abstract: | We characterize A-linear symmetric and contraction module operator semigroup {T t } t∈?+ ? L(l 2(A)), where A is a finite-dimensional C*-algebra, and L(l 2(A)) is the C*-algebra of all adjointable module maps on l 2(A). Next, we introduce the concept of operator-valued quadratic forms, and give a one to one correspondence between the set of non-positive definite self-adjoint regular module operators on l 2(A) and the set of non-negative densely defined A-valued quadratic forms. In the end, we obtain that a real and strongly continuous symmetric semigroup {T t } t∈?+ ? L(l 2(A)) being Markovian if and only if the associated closed densely defined A-valued quadratic form is a Dirichlet form. |
