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Paired Kernels and Their Applications
by
Partington, Jonathan R.
, Câmara, M. Cristina
in
Hilbert space
/ Mathematics
/ Mathematics and Statistics
/ Operators
/ Subspaces
2024
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Paired Kernels and Their Applications
by
Partington, Jonathan R.
, Câmara, M. Cristina
in
Hilbert space
/ Mathematics
/ Mathematics and Statistics
/ Operators
/ Subspaces
2024
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Journal Article
Paired Kernels and Their Applications
2024
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Overview
This paper considers paired operators in the context of the Lebesgue Hilbert space on the unit circle and its subspace, the Hardy space
H
2
. The kernels of such operators, together with their analytic projections, which are generalizations of Toeplitz kernels, are studied. Results on near-invariance properties, representations, and inclusion relations for these kernels are obtained. The existence of a minimal Toeplitz kernel containing any projected paired kernel and, more generally, any nearly
S
∗
-invariant subspace of
H
2
, is derived. The results are applied to describing the kernels of finite-rank asymmetric truncated Toeplitz operators.
Publisher
Springer International Publishing,Springer Nature B.V
Subject
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