Spectral theory of compact operators information

Hilbert space H, the compact operators are the closure of the finite rank operators in the uniform operator topology. In general, operators on infinite-dimensional...

limit of finite-rank operators, so that the class of compact operators can be defined alternatively as the closure of the set of finite-rank operators in...

Sturm–Liouville theory, Integral equations, Fredholm theory Compact operators, Isospectral operators, Completeness Spectral geometry Spectral graph theory List of functional...

general operators on infinite-dimensional spaces often requires a genuinely different approach. For example, the spectral theory of compact operators on Banach...

spaces. In general, the spectral theorem identifies a class of linear operators that can be modeled by multiplication operators, which are as simple as...

mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may...

a theorem on Fredholm operators. Part of the result states that a non-zero complex number in the spectrum of a compact operator is an eigenvalue. If V...

Hilbert–Schmidt operator, hence in particular is compact. V has no eigenvalues and therefore, by the spectral theory of compact operators, its spectrum...

operators are important because the spectral theorem holds for them. The class of normal operators is well understood. Examples of normal operators are...

structure of Fredholm's theory is given in terms of the spectral theory of Fredholm operators and Fredholm kernels on Hilbert space. The theory is named...

functional calculus Spectral theory Compact operator Laplace transform Fredholm theory Liouville–Neumann series Decomposition of spectrum (functional...

now known as Sturm–Liouville theory. In modern language, it is an application of the spectral theorem for compact operators due to David Hilbert. In his...

First notice that K is in L2(X, m), therefore T is compact. By the spectral properties of compact operators, any nonzero λ in σ(T) is an eigenvalue. But it...

mathematics, Fredholm operators are certain operators that arise in the Fredholm theory of integral equations. They are named in honour of Erik Ivar Fredholm...

spectral theory of these operators is similar to that of compact self-adjoint operators: any spectral value is real; they form a sequence tending to zero;...

this point of view, operator algebras can be regarded as a generalization of spectral theory of a single operator. In general operator algebras are non-commutative...

pseudodifferential operators. The spectral theory of unbounded self-adjoint operators is only marginally more difficult than for bounded operators. The spectrum of an...

(1959), Linear Operators. Part I: General Theory. Part II: Spectral Theory. Self Adjoint Operators in Hilbert Space. Part III: Spectral Operators., Pure and...

of functions defined on Hausdorff locally compact topological groups. One of the major results in the theory of functions on abelian locally compact groups...

operator. Compactness may be shown by invoking equicontinuity. As an operator, it has a spectral theory that can be understood in terms of a discrete...

summable spectral triple is a spectral triple (A, H, D) such that a.D for any a in A has a compact resolvent which belongs to the class of Lp+-operators for...

of the algebra of bounded operators on some Hilbert space. Measure algebra: A Banach algebra consisting of all Radon measures on some locally compact...