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On weakly formulated Sylvester equations and applications (CROSBI ID 118616)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Grubišić, Luka ; Veselić, Krešimir On weakly formulated Sylvester equations and applications // Integral equations and operator theory, 58 (2007), 2; 175-204. doi: 10.1007/s00020-007-1482-4

Podaci o odgovornosti

Grubišić, Luka ; Veselić, Krešimir

engleski

On weakly formulated Sylvester equations and applications

We use a ``weakly formulated'' Sylvester equation $$A^{; ; ; ; 1/2}; ; ; ; TM^{; ; ; ; -1/2}; ; ; ; -A^{; ; ; ; -1/2}; ; ; ; TM^{; ; ; ; 1/2}; ; ; ; =F$$ to obtain new bounds for the rotation of spectral subspaces of a nonnegative selfadjoint operator in a Hilbert space. Our bound extends the known results of Davis and Kahan. Another application is a bound for the square root of a positive selfadjoint operator which extends the known rule: ``The relative error in the square root is bounded by the one half of the relative error in the radicand''. Both bounds are illustrated on differential operators which are defined via quadratic forms.

eigenvalues ; eigenvectors ; variational methods for eigenvalues of operators ; perturbation theory

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Podaci o izdanju

58 (2)

2007.

175-204

objavljeno

0378-620X

1420-8989

10.1007/s00020-007-1482-4

Povezanost rada

Matematika

Poveznice
Indeksiranost