TY - JOUR

T1 - On projections in a space with an indefinite metric

AU - Hassi, Seppo

AU - Nordström, Kenneth

N1 - Funding Information:
This research was initiated while the second author was visiting Institut ftiMra thematik, Universitiit Augsburg, Germany, suppotied by grants of the Deutsche Forschungsgemeinschaft and the Academy of Finland. Sincere thanks go to Professor Friedrich Pukelsheim for the invitation.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1994

Y1 - 1994

N2 - We consider G-projectors (orthogonal projections) defined on an indefinite inner product space, and derive in a systematic way the indefinite counterparts of a number of useful results known to hold for ordinary projectors in Hilbert space. Some of the topological considerations encountered in the literature are avoided here, and several results are obtained using quite elementary matrix-type arguments. In particular, the relation between G-projectors and contractions in an indefinite inner product space is studied. For example, a convergence result is given for a nondecreasing sequence of G-contractive G-projectors. We also prove a result characterizing G-projectors within the class of idempotents, generalizing the corresponding result in Hilbert space.

AB - We consider G-projectors (orthogonal projections) defined on an indefinite inner product space, and derive in a systematic way the indefinite counterparts of a number of useful results known to hold for ordinary projectors in Hilbert space. Some of the topological considerations encountered in the literature are avoided here, and several results are obtained using quite elementary matrix-type arguments. In particular, the relation between G-projectors and contractions in an indefinite inner product space is studied. For example, a convergence result is given for a nondecreasing sequence of G-contractive G-projectors. We also prove a result characterizing G-projectors within the class of idempotents, generalizing the corresponding result in Hilbert space.

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U2 - 10.1016/0024-3795(94)90452-9

DO - 10.1016/0024-3795(94)90452-9

M3 - Article

AN - SCOPUS:21844498281

VL - 208-209

SP - 401

EP - 417

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - C

ER -