Multiplication-invariant operators and the classification of LCA group frames
نویسندگان
چکیده
In this paper we study the properties of multiplication invariant (MI) operators acting on subspaces vector-valued space L2(X;H). We characterize such in terms range functions by showing that there is an isomorphism between category MI spaces (with as morphisms) and measurable whose morphisms are operators. investigate how global operator reflected local pointwise its corresponding operator. also establish several results about frames generated multiplications This includes classification with respect to unitary equivalence fields Gramians. Finally, show applications our abelian group translation-invariant (TI) L2(G), where G a locally compact group.
منابع مشابه
Invariant subspaces of abstract multiplication operators
INVARIANT SUBSPACES OF ABSTRACT MULTIPLICATION OPERATORS by Hermann Flaschka We describe a class of operators on a Banach space ft whose members behave, in a sense, like multiplication operators, and consequently leave invariant a proper closed subspace of IB. One of the sufficient conditions for an operator to be such an "abstract multiplication" bears a striking resemblence to an assumption m...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2021
ISSN: ['0022-1236', '1096-0783']
DOI: https://doi.org/10.1016/j.jfa.2020.108780