Self-adjoint block operator matrices with non-separated diagonal entries and their Schur complements

H. Langer, A. Markus, V. Matsaev, C. Tretter

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

In this paper self-adjoint 2 × 2 block operator matrices A in a Hilbert space ℋ1 ⊕ ℋ2 are considered. For an interval which does not intersect the spectrum of at least one of the diagonal entries of A, we prove angular operator representations for the corresponding spectral subspace ℒ(,A) of A and we study the supporting subspace in this angular operator representation ℒ (A), which is the orthogonal projection of ℒ (A) to the corresponding component ℋ1 or ℋ2. Our main result is a description of a special direct complement of this supporting subspace in its component in terms of spectral subspaces of the values of the corresponding Schur complement of A in the endpoints of.

Original languageEnglish
Pages (from-to)427-451
Number of pages25
JournalJournal of Functional Analysis
Volume199
Issue number2
DOIs
StatePublished - 20 Apr 2003

Keywords

  • Angular operator
  • Block operator matrix
  • Schur complement

ASJC Scopus subject areas

  • Analysis

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