Singular Sylvester equation in Banach spaces and its applications: Fredholm theory approach

DOI10.1016/j.laa.2021.03.035OpenAlexW3146819455MaRDI QIDQ2029873

Bogdan D. Djordjević

Publication date: 4 June 2021

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2021.03.035

zbMATH Keywords

operator algebrasFredholm theorySylvester equations

Mathematics Subject Classification ID

Functional calculus for linear operators (47A60) (Semi-) Fredholm operators; index theories (47A53) Equations involving linear operators, with operator unknowns (47A62)

Related Items (6)

On the solvability of generalized Sylvester operator equations ⋮ On the solutions of the operator equation XAX  =  BX ⋮ Numerical solution of singular Sylvester equations ⋮ The Sylvester equation in Banach algebras ⋮ Singular Lyapunov operator equations: applications to \(C^*\)-algebras, Fréchet derivatives and abstract Cauchy problems ⋮ On the intrinsic structure of the solution set to the Yang-Baxter-like matrix equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Left-right Browder and left-right Fredholm operators
• Ruston, Riesz and perturbation classes
• On the operator equation \(BX - XA = Q\)
• The operator equation \(AX-XB=C\) with unbounded operators \(A\) and \(B\) and related abstract Cauchy problems
• Six generalized Schur complements
• Classes of linear operators. Vol. I
• Upper and lower Fredholm spectra. II
• Sylvester equations and projection-based model reduction.
• On the operator equation \(AX-XB=C\) with unbounded operators \(A\), \(B\), and \(C\)
• A characterization of commutators of idempotents
• Schur complements and state space realizations
• Equivalence after extension and Schur coupling coincide for inessential operators
• Generalized inverses. Theory and applications.
• Solving the operator equation \(AX-XB = C\) with closed \(A\) and \(B\)
• On a singular Sylvester equation with unbounded self-adjoint \(A\) and \(B\)
• Cauchy-Schwarz inequalities for inner product type transformers in \({Q}^*\) norm ideals of compact operators
• Inequalities for generalized derivations of operator monotone functions in norm ideals of compact operators
• Fréchet derivative and analytic functional calculus
• Inversion of operator pencils on Banach space using Jordan chains when the generalized resolvent has an isolated essential singularity
• On complementable operators in the sense of T. Ando
• Operator algebra generated by an element from the module \(\mathcal {B}(V_1,V_2)\)
• Equivalence after extension for compact operators on Banach spaces
• Bilateral shorted operators and parallel sums
• The fundamental equations for the generalized resolvent of an elementary pencil in a unital Banach algebra
• Theorems on ascent, descent, nullity and defect of linear operators
• Operators with finite ascent and descent
• ON LEFT AND RIGHT BROWDER OPERATORS
• On the Generalized Drazin Inverse and Generalized Resolvent
• Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†
• Upper and Lower Fredholm Spectra
• How and Why to Solve the Operator Equation AX −XB = Y
• H s -class construction of an almost invariant slow subspace for the Klein–Gordon equation in the non-relativistic limit
• Riesz Points of the Spectrum of an Element in a Semisimple Banach Algebra
• Solving the Sylvester Equation AX-XB=C when $\sigma(A)\cap\sigma(B)\neq\emptyset$
• Approximate Proper Vectors
• The Operator Equation BX - XA = Q with Selfadjoint A and B
• General Wiener-Hopf Operators
• Ascent, Descent, and Commuting Perturbations
• Classification and approximation of solutions to Sylvester matrix equation
• Spectral theory of linear operators and spectral systems in Banach algebras

This page was built for publication: Singular Sylvester equation in Banach spaces and its applications: Fredholm theory approach