Toeplitz算子的Fredholm性质

The Fredholm Properity of Toeplitz Operators

证明了以解析函数为符号的Ｔｏｅｐｌｉｔｚ算子是可逆的当且仅其符号可逆，描述了解析Ｔｏｅｐｌｉｔｚ算子是Ｆｒｅｄｈｏｌｍ算子时的符号特征．给出了一类符号的Ｔｏｅｐｌｉｔｚ算子是Ｆｒｅｄｈｏｌｍ算子的一些等价条件，指出紧Ｈａｎｋｅｌ算子符号是一闭子代数．

It is proved that Toeplitzs with analytic symbols to be inverse iff symbots are inverse. It gives the Fredholm Theory of Toeplitz operators on Bergman Space with analytic Symbols and gets equivalent conditions for a class of Toeplitzs to be Fredholm operators. It point out that symbols with compact Hankel operatohs are closed subalgehbras.