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Continuity of the eigenvalues of self-adjoint operators with respect to the strong operator topology

✍ Scribed by Joachim Weidmann

Publisher
SP Birkhäuser Verlag Basel
Year
1980
Tongue
English
Weight
133 KB
Volume
3
Category
Article
ISSN
0378-620X

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📜 SIMILAR VOLUMES

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The computation of eigenvalues and eigenvector of a completely continuous self-adjoint operator
✍ E.K. Blum 📂 Article 📅 1967 🏛 Elsevier Science 🌐 English ⚖ 307 KB

If A is a completely continuous self-adjoint operator on a Hilbert space, its eigen= values are the values of the inner product (Ax, x) at stationary points on the unit sphere. Gradient procedures can be used to determine eigenvectors and eigenvalues provided that certain regularity conditions hold

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Topological persistence of the normalized eigenvectors of a perturbed self-adjoint operator
✍ Raffaele Chiappinelli; Massimo Furi; Maria Patrizia Pera 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 370 KB

S the unit sphere of H. Assume that λ 0 is an isolated eigenvalue of T of odd multiplicity greater than 1. Given an arbitrary operator B:H → H of class C 1 , we prove that for any ε = 0 sufficiently small there exists x ε ∈ S and λ ε near λ 0 , such that Tx ε + εB(x ε ) = λ ε x ε . This result was c