## Inertia Theory for Operators on a Hilbert Space |

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### Contents

Generalized Stein and Lyapunov Theorems | 16 |

Inertia Theory for Hilbert Space | 36 |

Hermitian Stability and Hermitian | 61 |

1 other sections not shown

### Common terms and phrases

accessible from H AH is inertially arc of constant assume assumption Banach space BI(H BI(M BI(Mc Carlson chapter CnHCn condition cone with interior constant inertia defined denoted diagonal matrix dim(M dim(range Q equivalent exists an H finite dimensional gives gt>P H e BH H e BH(M H exists H is invertible Hence Hermitian operator Hermitian semi-stable Hermitian stable Hilbert space Hx,x implies im(A)x,x In(A In(AH In(B In(H INERTIA THEORY inertially accessible invariant subspace isometrically isomorphic Kre(A)K Kx,x Lemma Lyapunov Theorem mapping matrices Notational Preliminaries null space Ostrowski and Schneider P)BP Proposition proved re(AH real numbers sequence sp(A sp(AH sp(B sp(C sp(H sp(I sp(KAK spectral radius spectral set Spectral Theorem sr(C Stein Theorem Suppose Theorem for matrices Theorem l3 unitary operators v e sp(T V(KAK x e S(M