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Localised frames for tensor product spaces
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DOI：10.1007/s00605-026-02184-4.png)
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Abstract
En 中文
In this paper, we investigate whether the tensor product of two frames, each individually localised with respect to a spectral matrix algebra, is also localised with respect to a suitably chosen tensor product algebra. We provide a partial answer by constructing an involutive Banach algebra of rank-four tensors that is built from two solid spectral matrix algebras. We show that this algebra is inverse-closed, given that the original algebras satisfy a specific property related to operator-valued versions of these algebras. This condition is satisfied by all commonly used solid spectral matrix algebras. We then prove that the tensor product of two self-localised frames remains self-localised with respect to our newly constructed tensor algebra. Additionally, we discuss generalisations to localised frames of Hilbert-Schmidt operators, which may not necessarily consist of rank-one operators.
Keywords:
Localised frames
Tensor products
Spectral matrix algebras
Inverse-closedness
Journal
M
IF:
0.8
Papers:
67
Citations:
0