Toeplitz Operators on Semi-Simple Lie Groups

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:
Hermitescher symmetrischer Raum
Invariant cone
Jordan-Tripelsystem
Hermitian symmetric space
Jordan triple system
Face
Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
Hardyy space
Mathematik
Toeplitz algebra
Toeplitz-Algebra
Hardy-Raum
Diskrete Reihe
Hopf-Algebra
Halbeinfache Lie-Gruppe
Mathematics
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Summary: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 $T$ associated to boundary strata of the domain $\Gamma$.
Physical Description:254 Pages
DOI:10.17192/z2005.0511

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