## Perturbation Matrices for Finitely Perturbed Banach Systems |

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algebraic Banach spaces chains of type character choose a basis closed unbounded operations compact connected subset complete spectral decomposition component construction of Vq decomposition of G Define linear transformation defined and analytic divisor G eigenspace elementary divisors equation finite dimensional perturbation FINITELY PERTURBED BANACH form a non-decreasing Fredholm domain Fredholm set G-XH geometric multiplicity Hilbert space i=l i=l induction isolated eigenvalue Let G Let the Banach linearly independent matrix M(X minimal system minors of M(X mj mj mj modulo Vq Mq(X MX(X Note null space obtain perturbation matrix 3.1 perturbation matrix defined PERTURBED BANACH SYSTEMS present paper proof of Proposition Proposition 2.1 Remark resolvent set respect to G row or column row vector set of elementary set of G spect subspaces system G systems of type Theorem 5.1 type of M(X YQ 9 YQ to XQ