If b is an inner function, then composition with b induces an endomorphism, beta, of Linfinity ( T ) that leaves Hinfinity( T ) invariant. In this document we investigate the structure of the endomorphisms of B(L2( T )) and B(H2( T )) that implement beta via the representations of L infinity( T ) and Hinfinity( T ) in terms of multiplication operators on B( L2( T )) and B(H2( T )). Our analysis, which was inspired by the work of R. Rochberg and J. McDonald, will range from the theory of composition operators on spaces of analytic functions to recent work on Cuntz families of isometries and Hilbert C*-modules.
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机译：如果b是一个内部函数，则与b的组合会诱导Linfinity（T）的内胚性β，从而使Hinfinity（T）不变。在本文中，我们研究了B（L2（T））和B（H2（T））的内态结构，该结构通过B上的乘法算符通过L infinity（T）和Hinfinity（T）的表示来实现beta （L2（T））和B（H2（T））。受R. Rochberg和J. McDonald的研究启发，我们的分析范围从分析函数空间上的合成算符理论到有关Cuntz族的等距和Hilbert C *-模块的最新工作。
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