A Noncommutative Wiener Lemma and A Faithful Tracial State on Banach Algebras of Time-Frequency Shift Operators

Details A Noncommutative Wiener Lemma and A Faithful Tracial State on Banach Algebras of Time-Frequency Shift Operators A Noncommutative Wiener Lemma and A Faithful Tracial State on Banach Algebras of Time-Frequency Shift Operators

2005-10-10

arxiv.org/abs/math/0510178v1

Mathematics

Functional Analysis

Scientific paper

In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also construct a faithful tracial state on this algebra which implies the algebra contains no compact operators. As a corollary we obtain a special case of the Heil-Ramanathan-Topiwala conjecture regarding linear independence of finitely many time-frequency shifts of one $L^2$ function.

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