This work demonstrates the convergence of convolution operators in additive-invariant Banach spaces, suggesting new insights for positive approximate identity.
Analog of Korovkin type theorem for the sequence of convolution operators in the subspaces of additive-invariant Banach spaces generated by the shift operator is obtained in this work. Convergence to the identity of the sequence of convolution operators with a positive approximate identity is proved. We also prove the convergence to the identity of Steklov operators in Marcinkiewicz spaces.
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Исмайлов et al. (2025) studied this question.
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