Abstract
We show that the kernel and/or cokernel of a block Toeplitz operator T (G) are trivial if its matrix-valued symbol G satisfies the condition \(G(t^{-1})G(t)^*\;=\;I_N\). As a consequence, the Wiener–Hopf factorization of G (provided it exists) must be canonical. Our setting is that of weighted Hardy spaces on the unit circle. We extend our result to Toeplitz operators on weighted Hardy spaces on the real line, and also Toeplitz operators on weighted sequence spaces.
Mathematics Subject Classification (2010). Primary 47B35. Secondary 47A68, 47B30.
To Professor Leonia Lerer, in celebration of his seventieth birthday.
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Ehrhardt, T., Spitkovsky, I.M. (2013). On the Kernel and Cokernel of Some Toeplitz Operators. In: Kaashoek, M., Rodman, L., Woerdeman, H. (eds) Advances in Structured Operator Theory and Related Areas. Operator Theory: Advances and Applications, vol 237. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0639-8_10
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DOI: https://doi.org/10.1007/978-3-0348-0639-8_10
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