et ]Ibe a bounded symmetric domain, f2 C ]Ia bounded subdomain, and let 7-[2 C L2 denote the weighted Bergman space of holomorphic square integrable functions on II. Let Tx,g2 be the Berezin-Toeplitz operator on 7-t2 with symbol X~2 and kth eigenvalue 3.k(T~,~2). We prove that for 31 sufficiently close to 0 and 32 sufficiently close to 1 the estimate Cll~[ _<#{kl~l <~2}< e21~21 holdsfor all domains [2satisfying the condition ]{zE11I d(z, f2) < e}l _
Localization type Berezin--Toeplitz operators on bounded symmetric domains
DE MARI CASARETO DAL VERME, FILIPPO;
2002-01-01
Abstract
et ]Ibe a bounded symmetric domain, f2 C ]Ia bounded subdomain, and let 7-[2 C L2 denote the weighted Bergman space of holomorphic square integrable functions on II. Let Tx,g2 be the Berezin-Toeplitz operator on 7-t2 with symbol X~2 and kth eigenvalue 3.k(T~,~2). We prove that for 31 sufficiently close to 0 and 32 sufficiently close to 1 the estimate Cll~[ _<#{kl~l <~2}< e21~21 holdsfor all domains [2satisfying the condition ]{zE11I d(z, f2) < e}l _
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