Products of orthogonal projections as Carleman operators |
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Authors: | Manuela Nees |
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Institution: | (1) Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstr. 1 1/2, D-91054 Erlangen, Germany |
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Abstract: | In this paper, we consider the product of two orthogonal projectionsP andQ on a separable, infinite dimensional Hilbert spaceH. For the operatorQP, there holds the dichotomy:QP is either a Carleman operator or a semi-Fredholm operator with finite defect. Both cases are characterized in terms of the dimensions of the ranges and null spaces ofP andQ and some of their intersections. This extends the case, whereP andQ are the special projections onto the subspaces of time- and band-limited functions inL
2( ) resp., first considered by Slepian, Pollak and Landau. |
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Keywords: | 47A05 47A53 47G10 46C05 47B99 |
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