Spectral gap of positive operators and applications

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Existence of the Spectral Gap for Elliptic Operators

Let M be a connected, noncompact, complete Riemannian manifold, consider the operator L = ∆+∇V for some V ∈ C(M) with exp[V ] integrable w.r.t. the Riemannian volume element. This paper studies the existence of the spectral gap of L. As a consequence of the main result, let ρ be the distance function from a point o, then the spectral gap exists provided limρ→∞ supLρ < 0 while the spectral gap d...

Spectral Theorem for Normal Operators: Applications

In these notes, we present a number of interesting and diverse applications of the Spectral Theorem for Normal Operators. These include a Spectral Mapping Theorem for Normals Operators, a Spectral Characterization of Algebraic Operators, von Neumann’s Mean Ergodic Theorem, Pathconnectivity of the Group of Invertible Operators, and some Polynomial Approximation Results for Operators.

A New Spectral Theory for Nonlinear Operators and Its Applications

In this paper, by applying (p, k)-epi mapping theory, we introduce a new definition of spectrum for nonlinear operators which contains all eigenvalues, as in the linear case. Properties of this spectrum are given and comparison is made with the other definitions of spectra. We also give applications of the new theory.

Lecture 18 : Normal operators , the spectral theorems , isometries , and positive operators ( 1 )