Triple variational principles for self-adjoint operator functions

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• 作者：Matthias Langer^a ; ^{m.langer@strath.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Michael Strauss^b ; ^{m.strauss@sussex.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 49R05 ; secondary ; 47A56 ; 47A10
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：15 March 2016
• 年：2016
• 卷：270
• 期：6
• 页码：2019-2047
• 全文大小：527 K

文摘

For a very general class of unbounded self-adjoint operator functions we prove upper bounds for eigenvalues which lie within arbitrary gaps of the essential spectrum. These upper bounds are given by triple variations. Furthermore, we find conditions which imply that a point is in the resolvent set. For norm resolvent continuous operator functions we show that the variational inequality becomes an equality.