On Schatten-class perturbations of Toeplitz operators

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• 作者：Michael Didas ^{didas@math.uni-sb.de} ; J&ouml ; rg Eschmeier ; ^{eschmei@math.uni-sb.de} ; Dominik Schillo ^{schillo@math.uni-sb.de}
• 关键词：47A13 ; 47B20 ; 47B35 ; 47L80 ; 47B47
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：272
• 期：6
• 页码：2442-2462
• 全文大小：402 K
• 卷排序：272

文摘

Let D   denote the unit ball or the unit polydisc in CnCn with n≥2n≥2. For 1≤p≤2n1≤p≤2n in the case of the ball and 1≤p<∞1≤p<∞ for the polydisc, we show that a bounded operator S   on the Hardy space H2(D)H2(D) commutes with all analytic Toeplitz operators modulo the Schatten class SpSp if and only if S=X+KS=X+K with an analytic Toeplitz operator X   and an operator K∈SpK∈Sp. This partially answers a question of Guo and Wang [14]. For 1≤p<∞1≤p<∞ and a strictly pseudoconvex or bounded symmetric and circled domain D⊂CnD⊂Cn, we show that a given operator S   on H2(D)H2(D) is a Schatten-p  -class perturbation of a Toeplitz operator if and only if Tθ⁎STθ−S∈Sp for every inner function θ on D.