On a class of operators with finiterank self-commutators |
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| Authors: | Daoxing Xia |
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| Institution: | (1) Department of Mathematics, Vanderbilt University, 37240 Nashville, TN, USA |
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| Abstract: | This paper studies the class of pure operatorsA on a Hilbert space
satisfying dimK
A
< , where
![$$K_A = V_{n = 0}^\infty A^{*n} A^* ,A]\mathcal{H}$$](/content/j88558894317196g/20_2005_Article_BF01291839_TeX2GIFIE2.gif)
. The main tool is a pair of matrices
![$$C_A = A^* ,A]_{K_A }$$](/content/j88558894317196g/20_2005_Article_BF01291839_TeX2GIFIE3.gif)
and
. A reproducing kernel Hilbert space model is introduced for a subclass of this class of operators. Some theorems are established for some subnormal operators as well as hyponormal operators in this class. |
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| Keywords: | (1985 Revision) Primary 47B20 |
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