Closedness of the Rang of the Product of Projections in Hilbert Modules

Volume 2, Issue 4, pp 588--593 http://dx.doi.org/10.22436/jmcs.02.04.03

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Authors

Kamran Sharifi - Department of Mathematics, Shahrood University of Technology, P. O. Box 3619995161-316, Shahrood, Iran

Abstract

Suppose P and Q are orthogonal projections between Hilbert C*-modules, then PQ has closed range if and only if Ker(P)+Ran(Q) is an orthogonal summand, Ker(Q)+ Ran(P) is an orthogonal summand.

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Keywords

• Hilbert C*-module
• projection
• Moore-Penrose inverse
• closed range.

MSC

•  46L08
•  47A05
•  15A09
•  46L05

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