Disintegration of bounded quasi-positive Hilbert forms

Disintegration of bounded quasi-positive Hilbert forms Positivity 6: 191–200, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands. Disintegration of bounded quasi-positive Hilbert forms TORBEN MAACK BISGAARD Nandrupsvej 7 st. th., DK-2000 Frederiksberg C, Denmark. E-mail: torben.bisgaard@get2net.dk (Received 8 May 2000; accepted 4 March 2001) 1. Introduction Suppose A is a ∗-algebra, it being understood that the scalar ﬁeld is the ﬁeld of complex numbers. Suppose ·, · is a Hilbert form on A, that is, a hermitian sesquilinear form having the shift property ab, c= b, a c for all a, b, c ∈ A. All of the following deﬁnitions are relative to ·, ·. A linear subspace E of A is negative (resp. positive)if a, a < 0 (resp.  0) for all a ∈ E\{0}.If E is positive then we also say that ·, · is positive on E.The number of negative squares of ·, · is the maximal dimension of any ﬁnite-dimensional negative sub- space, or ∞ if there is no maximum. The form ·, · is quasi-positive if it has only ﬁnitely many negative squares. A deﬁnitizing ideal for ·, · is a positive left ideal of A. For linear subspaces I and J of A, denote by IJ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Disintegration of bounded quasi-positive Hilbert forms

, Volume 6 (2) – Oct 14, 2004
10 pages

/lp/springer_journal/disintegration-of-bounded-quasi-positive-hilbert-forms-gb4jZU9xGZ
Publisher
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1015236030333
Publisher site
See Article on Publisher Site

Abstract

Positivity 6: 191–200, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands. Disintegration of bounded quasi-positive Hilbert forms TORBEN MAACK BISGAARD Nandrupsvej 7 st. th., DK-2000 Frederiksberg C, Denmark. E-mail: torben.bisgaard@get2net.dk (Received 8 May 2000; accepted 4 March 2001) 1. Introduction Suppose A is a ∗-algebra, it being understood that the scalar ﬁeld is the ﬁeld of complex numbers. Suppose ·, · is a Hilbert form on A, that is, a hermitian sesquilinear form having the shift property ab, c= b, a c for all a, b, c ∈ A. All of the following deﬁnitions are relative to ·, ·. A linear subspace E of A is negative (resp. positive)if a, a < 0 (resp.  0) for all a ∈ E\{0}.If E is positive then we also say that ·, · is positive on E.The number of negative squares of ·, · is the maximal dimension of any ﬁnite-dimensional negative sub- space, or ∞ if there is no maximum. The form ·, · is quasi-positive if it has only ﬁnitely many negative squares. A deﬁnitizing ideal for ·, · is a positive left ideal of A. For linear subspaces I and J of A, denote by IJ

Journal

PositivitySpringer Journals

Published: Oct 14, 2004

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