李绍宽
Abstract
In Ref. it is proved that for Toeplitz operator T_φ and Hankel operator H_ψ on Hardy space H~2(T) if R(T_φ)R(H_ψ), then T_φ=0. In this note we will discuss similar problem for the Toeplitz operators and Hankel operators related with the shifts. The result extended not only to the general case, but also to the Beurling problem.
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In Ref. it is proved that for Toeplitz operator T_φ and Hankel operator H_ψ on Hardy space H~2(T) if R(T_φ)R(H_ψ), then T_φ=0. In this note we will discuss similar problem for the Toeplitz operators and Hankel operators related with the shifts. The result extended not only to the general case, but also to the Beurling problem.
Key concepts: Toeplitz matrix, Mathematics, Hankel matrix, Hardy space, Toeplitz operator, Operator (biology), Pure mathematics, Algebra over a field