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Ein neues Surjektivitätskriterium im Hilbertraum

A new criterion for surjectivity in Hilbert spaces

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Abstract

LetA, B andC be linearm-accretive operators in a Hilbert space. Suppose further thatC is bounded, thatb:=inf {Re (C y, y)| ∥y∥=1}>0, thatA −1 exists as a bounded operator and that Re (B * x, A −1 x)+a ∥x∥2≥0 holds for allx∈D (B *) and a constanta with 0≤a<b. ThenCA+B is surjective, (CA+B)−1 exists and ∥C Ax+Bx∥≥ ≥(b−a) ∥A x∥ holds for allx∈D (A) ∩D (B). This criterion can be applied to evolution equations of the formdu/dt+C(t)A(t)u=f(t) whereB:=d/dt.

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Authors and Affiliations

  1. Fachbereich Mathematik der Universität-Gesamthochschule, Warburger Straße 100, D-7490, Paderborn, Bundesrepublik Deutschland

    Hermann Sohr

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  1. Hermann Sohr
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Sohr, H. Ein neues Surjektivitätskriterium im Hilbertraum. Monatshefte für Mathematik 91, 313–337 (1981). https://doi.org/10.1007/BF01294771

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  • DOI: https://doi.org/10.1007/BF01294771

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