A Contractive Operator View on an Inversion Formula of Gohberg-Heinig
This paper presents a contractive operator view on the inversion formula for finite Toeplitz operator matrices due to Gohberg-Heinig. The general setting that will be used involves a Hilbert space operator T and a contraction A such that the compression of T - A*TA to the orthogonal complement of the defect space of A is the zero operator. For such an operator T the analogue of the Gohberg-Heinig inversion formula is obtained. The main results are illustrated on various special cases, including Toeplitz plus Hankel operators and model operators.
KeywordsGohberg-Heinig inversion formula Toeplitz operator matrices contractive operators Toeplitz plus Hankel operators compression of Toeplitz operators model operators Stein equation
Mathematics Subject Classification (2000).Primary 47A45 47A50 47B35
Secondary 15A0947A20 65F05
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