We discuss criteria for the affiliation of a self-adjoint operator to a C*-algebra. We consider in particular the case of graded C*-algebras and we give applications to Hamiltonians describing the motion of dispersive N-body systems and the wave propagation in pluristratified media.
In this article we investigate the essential spectra of a 2 × 2 block operator matrix on a Banach space. Furthermore, we apply the obtained results to determine the essential spectra of two-group transport operators with general boundary conditions in the Banach space L p ([−a, a] × [−1, 1]) × L p ([−a, a] × [−1, 1]), a > 0.
In this work, we present a new concept of measure-ergodic process to define
the space of measure pseudo almost periodic process in the p-th mean sense.
We show some results regarding the completeness, the composition theorems
and the invariance of the space consisting in measure pseudo almost periodic
process. Motivated by above mentioned results, the Banach fixed point
theorem and the stochastic analysis techniques, we prove the existence,
uniqueness and the global exponential stability of doubly measure pseudo
almost periodic mild solution for a class of nonlinear delayed stochastic
evolution equations driven by Brownian motion in a separable real Hilbert
space. We provide an example to illustrate the effectiveness of our results.
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