Trace class perturbation of closed linear relations
نویسندگان
چکیده
This paper studies trace class perturbation of closed linear relations in Hilbert spaces. The concept is introduced by orthogonal projections. Equivalent characterizations compact and block operator matrices are first given terms their elements, separately. By using them, several equivalent sufficient obtained.
منابع مشابه
Solving a class of linear and non-linear optimal control problems by homotopy perturbation method
In this paper, we give an analytical approximate solution for non-linear quadratic optimal control problems and optimal control of linear systems using the homotopy perturbation method (HPM). Applying the HPM, the non-linear two-point boundary-value problem (TPBVP) and linear systems, derived from the Pontryagin’s maximum principle, are transformed into a sequence of linear time-invariant TPBVP...
متن کامل⊤⊤-closed relations and admissibility
While developing a method for reasoning about programs, Pitts defined the ⊤⊤-closed relations as an alternative to the standard admissible relations. This paper reformulates and studies Pitts’s operational concept of ⊤⊤-closure in a semantic framework. It investigates the nontrivial connection between ⊤⊤-closure and admissibility, showing that ⊤⊤-closure is strictly stronger than admissibility ...
متن کاملContinuity and General Perturbation of the Drazin Inverse for Closed Linear Operators
In this paper, we investigate a perturbation of the Drazin inverse AD of a closed linear operator A; the main tool for obtaining the estimates is the gap between subspaces and operators. By (X) we denote the set of all closed linear operators acting on a linear subspace of X to X , where X is a complex Banach space. We write (A), (A), (A), ρ(A), σ(A), and R(λ,A) for the domain, nullspace, range...
متن کاملRecognizing Trace Graphs of Closed Braids
To a closed braid in a solid torus we associate a trace graph in a thickened torus in such a way that closed braids are isotopic if and only if their trace graphs can be related by trihedral and tetraherdal moves. For closed braids with a fixed number of strands, we recognize trace graphs up to isotopy and trihedral moves in polynomial time with respect to the braid length.
متن کاملControlled linear perturbation
We present a new approach to the robustness problem in computational geometry, called controlled linear perturbation, and demonstrate it on Minkowski sums of polyhedra. The robustness problem is how to implement real RAM algorithms accurately and efficiently using computer arithmetic. Approximate computation in floating point arithmetic is efficient but can assign incorrect signs to geometric p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2021
ISSN: ['1873-1856', '0024-3795']
DOI: https://doi.org/10.1016/j.laa.2020.10.022