Abstract

AbstractWe give a simple characterization of when the product of two infinite block Toeplitz matrices is another infinite block Toeplitz matrix. We then use this characterization to answer the question of when two infinite block Toeplitz matrices commute. This approach gives a unified treatment for two related problems which are often studied separately for infinite scalar Toeplitz-like and Hankel-like matrices. Related results for products of two infinite block Hankel matrices are also obtained.KeywordsToeplitz matrixHankel matrixBlock Toeplitz operatorBlock Hankel operator

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