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M. Malamud (2003)
Similarity of a Triangular Operator to a Diagonal OperatorJournal of Mathematical Sciences, 115
S. Parter, S. Wong (1991)
Preconditioning second-order elliptic operators: Condition numbers and the distribution of the singular valuesJournal of Scientific Computing, 6
S. Chandler-Wilde, I. Graham, S. Langdon, M. Lindner (2009)
Condition number estimates for combined potential boundary integral operators in acoustic scatteringJournal of Integral Equations and Applications, 21
M Seidel, B Silbermann (2013)
Finite sections of band-dominated operators, norms, condition numbers and pseudospectra, Operator Theory: Advances and Applications
M. Gil' (2014)
A BOUND FOR SIMILARITY CONDITION NUMBERS OF UNBOUNDED OPERATORS WITH HILBERT–SCHMIDT HERMITIAN COMPONENTSJournal of the Australian Mathematical Society, 97
T Betcke, SN Chandler-Wilde, IG Graham, S Langdon (2011)
Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation, NumerMethods Partial Diff. Equ., 27
IM Karabash, AS Kostenko, MM Malamud (2009)
The similarity problem for J-nonnegative SturmLiouville operatorsJ. Differ. Equ., 246
A. Kostenko (2010)
The similarity problem for indefinite Sturm-Liouville operators with periodic coefficientsarXiv: Spectral Theory
MM Faddeev, RG Shterenberg (2002)
On similarity of differential operators to a selfadjoint oneMath. Notes, 72
Benoît Pruvost (2002)
Analytic equivalence and similarity of operatorsIntegral Equations and Operator Theory, 44
Markus Seidel, B. Silbermann (2013)
Finite Sections of Band-dominated Operators – Norms, Condition Numbers and Pseudospectra
(2000)
J -selfadjoint ordinary differential operators similar to selfadjoint operators
Guoliang Chen, Yimin Wei, Yifeng Xue (2004)
The generalized condition numbers of bounded linear operators in Banach spacesJournal of the Australian Mathematical Society, 76
T. Betcke, S. Chandler-Wilde, I. Graham, S. Langdon, M. Lindner (2010)
Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisationNumerical Methods for Partial Differential Equations, 27
Illia Karabash, A. Kostenko, M. Malamud
Institute for Mathematical Physics the Similarity Problem for J–nonnegative Sturm–liouville Operators the Similarity Problem for J-nonnegative Sturm-liouville Operators
F. Smithies (1954)
Linear OperatorsNature, 174
SN Chandler-Wilde, IG Graham, S Langdon, M Lindner (2009)
Condition number estimates for combined potential boundary integral operators in acoustic scatteringJ. Int. Eqn. Appl., 21
A. Kostenko (2012)
The similarity problem for indefinite Sturm–Liouville operators and the HELP inequalityAdvances in Mathematics, 246
J. Casteren (1983)
Operators similar to unitary or selfadjoint onesPacific Journal of Mathematics, 104
Tosio Kato (1966)
Perturbation theory for linear operators
M. Gil' (1999)
Perturbations of simple eigenvectors¶of linear operatorsmanuscripta mathematica, 100
Nourelhouda Benamara, N. Nikolski (1999)
Resolvent Tests for Similarity to a Normal OperatorProceedings of the London Mathematical Society, 78
We consider a linear unbounded operator $$A$$ A in a separable Hilbert space. with the following property: there is a normal operator $$D$$ D with a discrete spectrum, such $$\Vert A-D\Vert <\infty $$ ‖ A - D ‖ < ∞ . Besides, all the Eigen values of $$D$$ D are different. Under certain assumptions it is shown that $$A$$ A is similar to a normal operator and a sharp bound for the condition number is suggested. Applications of that bound to spectrum perturbations and operator functions are also discussed. As an illustrative example we consider a non-selfadjoint differential operator.
Analysis and Mathematical Physics – Springer Journals
Published: Mar 7, 2015
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