Approximations of self-adjoint \(C_0\)-semigroups in the operator-norm topology

Continuity of Cp-semigroups in the Point-strong Operator Topology

We prove that if {φt}t≥0 is a CP-semigroup acting on a von Neumann algebra M ⊆ B(H), then for every A ∈ M and ξ ∈ H , the map t 7→ φt(A)ξ is norm-continuous. We discuss the implications of this fact to the existence of dilations of CPsemigroups to semigroups of endomorphisms.

The Laplace operator is essentially self-adjoint

The norm of the non-self-adjoint harmonic oscillator semigroup

We identify the norm of the semigroup generated by the non-selfadjoint harmonic oscillator acting on L2(R), for all complex times where it is bounded. We relate this problem to embeddings between Gaussian-weighted spaces of holomorphic functions, and we show that the same technique applies, in any dimension, to the semigroup e−tQ generated by an elliptic quadratic operator acting on L2(Rn). The...

Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator

We prove that the eigenvalues of a certain highly non-self-adjoint operator that arises in fluid mechanics correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are infinitely many real eigenvalues which accumulate only at ±∞. We use this result to determine the asymptotic distribution of the eigenvalues and to compute some of ...

the relationship between academic self-concept and academic achievement in english and general subjects of the students of high school

according to research, academic self-concept and academic achievement are mutually interdependent. in the present study, the aim was to determine the relationship between the academic self-concept and the academic achievement of students in english as a foreign language and general subjects. the participants were 320 students studying in 4th grade of high school in three cities of noor, nowshah...