Abstract

    Open Access Short Communication Article ID: AMP-7-232

    Rayleigh Quotient and Surjectivity of Nonlinear Operators in Hilbert space

    Raffaele Chiappinelli*

    We consider continuous operators acting in a real Hilbert space and indicate conditions ensuring their continuous invertibility and/or surjectivity. In the case of bounded linear operators, these facts are well-known from basic Functional Analysis. The objective of this work is to indicate how similar properties can be proved also when the operators are not necessarily linear, using as a main tool their Rayleigh quotient and especially its lower and upper bound. In particular, we focus our attention on gradient operators and show a quantitative criterion that ensures their surjectivity through the positivity of an additional constant related to the measure of noncompactness. 

    Keywords:

    Published on: Sep 28, 2024 Pages: 277-278

    Full Text PDF Full Text HTML DOI: 10.17352/amp.000132
    CrossMark Publons Harvard Library HOLLIS Search IT Semantic Scholar Get Citation Base Search Scilit OAI-PMH ResearchGate Academic Microsoft GrowKudos Universite de Paris UW Libraries SJSU King Library SJSU King Library NUS Library McGill DET KGL BIBLiOTEK JCU Discovery Universidad De Lima WorldCat VU on WorldCat

    Indexing/Archiving

    Pinterest on AMP