A STRONG OPERATOR TOPOLOGY ADIABATIC THEOREM

A Strong Operator Topology Adiabatic Theorem

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We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation in the context of a system without an intrinsic time scale. For continuous functions of the unperturbed Hamiltonian the convergence is in norm while for a larger class functions, including the spectral projections associated to embedded eigenvalues, the convergence is in the strong operator topol...

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We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation. For continuous functions of the unperturbed Hamiltonian the convergence is in norm while for a larger class functions, including the spectral projections associated to embedded eigenvalues, the convergence is in the strong operator 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.

Strong convergence theorem for solving split equality fixed point problem which does not involve the prior knowledge of operator norms

‎Our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove a strong convergence theorem for approximating a solution of split equality fixed point problem for quasi-nonexpansive mappings in a real Hilbert space‎. ‎So many have used algorithms involving the operator norm for solving split equality fixed point problem‎, ‎...