there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.

We provide a generalization of Lieb’s triple matrix extension the Golden–Thompson inequality from algebras to setting traces on finite von Neumann algebras. More precisely, assume that ℳ is algebra equipped with tracial state τ. If 1≤p,q≤∞ 1/p+1/q=1, it shown whenever a, b, and c are self-adjoint τ-measurable operators satisfying a∈ℳ, e b ∈L p (ℳ,τ), q then following holds:

Using Dirac equation together with the Wigner distribution function,the trembling motion,known as Zitterbewegung effect,of moving electrons in quasi-one-dimensional relativistic quantum plasma is theoretically investigated.The matrix used to calculate mean values of position and velocity operators for a gas electrons.It found that oscillatory behavior measurable quantities could be associated e...

An essentially unique homeomorphic solution to the Beltrami equation with measurable coefficients was found in 1930s by Morrey. The most well-known proof from 1960s uses theory of Calderón–Zygmund and singular integral operators $$L^p(\mathbb {C})$$ . We will present an alternative method solve using Hodge star operator standard elliptic PDE theory. also discuss a different prove regularity sol...

In this paper, we focus on a family of backward stochastic differential equations (BSDEs) with subdifferential operators that are driven by infinite-dimensional martingales. We shall show the solution to such BSDEs exists and is unique. The existence uniqueness established using Yosida approximations. Furthermore, as an application main result, partial equation martingales continuous linear ope...