Toeplitz Operators on Semi-Simple Lie Groups

Let $G/K$ be a Hermitian symmetric space of non-compact type. We consider for the so-called minimal Olshanskii semigroup $\Gamma\subset G^C$, the C$^*$-algebra $T$ generated by all Toeplitz operators $T_f$ on the Hardy space $H^2(\Gamma)\subset L^2(G)$. We describe the construction of ideals of $T$...

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Bibliographic Details

Main Author:	Alldridge, Alexander
Contributors:	Upmeier, Harald (Prof. Dr.) (Thesis advisor)
Format:	Doctoral Thesis
Language:	English
Published:	Philipps-Universität Marburg 2004
Subjects:	Hardyy space Hermitescher symmetrischer Raum Hermitian symmetric space Jordan-Tripelsystem Invariant cone Face Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) Mathematik Toeplitz-Algebra Hardy-Raum Jordan triple system Diskrete Reihe Toeplitz algebra Hopf-Algebra Halbeinfache Lie-Gruppe Mathematics
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