2026-09-20T15:45:37Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/71247 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Butler, Charles Allen 2014-12-16T06:18:17Z 2014-12-16T06:18:17Z 10000-01-01 1987 1987 The Schur complement of a linear operator on a finite dimensional Hilbert space is discussed and six generalizations are presented. Conditions are established under which these generalizations are equivalent. The infinite dimensional case is then considered and counterexamples are given to show that not all the generalizations extend in a natural way. An approximating sequence is shown to exist for the Schur complement matrix equation. The sequences which work as approximating sequences are classified. Finally, an application to infinite ladder networks of operators is given. Made available in DSpace on 2014-12-16T06:18:17Z (GMT). No. of bitstreams: 1 8711776.pdf: 1952608 bytes, checksum: a1fec23d895270dc75610fc472fc7980 (MD5) Previous issue date: 1987 Embargo set by: Seth Robbins for item 71413 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 78 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987. http://hdl.handle.net/2142/71247 (UMI)AAI8711776 Mathematics Approximation of Generalized Schur Complements (Ladder Network) text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.