2006
DOI: 10.1090/s0002-9947-06-03841-4
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Symmetry and inverse-closedness of matrix algebras and functional calculus for infinite matrices

Abstract: Abstract. We investigate the symbolic calculus for a large class of matrix algebras that are defined by the off-diagonal decay of infinite matrices. Applications are given to the symmetry of some highly non-commutative Banach algebras, to the analysis of twisted convolution, and to the theory of localized frames.

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Cited by 101 publications
(92 citation statements)
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“…So far, we considered operators (infinite matrices) Φ τ δ , produced from a function φ with a certain decay rate (4). It turns out that all these operators belong in the Gröchenig-Shur class A p,u α [20] which contains operators A = {a m,n } m,n∈Z with norm…”
Section: Local Sampling and Approximationmentioning
confidence: 99%
See 1 more Smart Citation
“…So far, we considered operators (infinite matrices) Φ τ δ , produced from a function φ with a certain decay rate (4). It turns out that all these operators belong in the Gröchenig-Shur class A p,u α [20] which contains operators A = {a m,n } m,n∈Z with norm…”
Section: Local Sampling and Approximationmentioning
confidence: 99%
“…For more details about Wiener's lemma for infinite matrices, we refer to [20,26,34,35], and for an excellent overview on Wiener's lemma and its variations, we refer to [22] and references therein. The bound (19) enables us to deduce that the Riesz basis {ψ τ δ n } n∈Z associated to the reconstruction formula ( 15) inherits the decay rate form φ.…”
Section: Now We Havementioning
confidence: 99%
“…First we define the standard classes of matrices with off‐diagonal decay. For more comprehensive treatments see, e.g., , , , , . In the following A is always a matrix over the index set double-struckZ with entries A(k,l),k,lZ.…”
Section: Norm‐controlled Inversion In Matrix Algebras With Off‐ Diagomentioning
confidence: 99%
“…The simplest case of a trivial action leads to the projective tensor product between L 1 (G) and a C * -algebra. Some references are: [20,4,18,23,22,14,15,3,12,13,5,21,11].…”
Section: Introductionmentioning
confidence: 99%