A Noncommutative Wiener Lemma and A Faithful Tracial State on Banach Algebras of Time–Frequency Shift Operators
نویسندگان
چکیده
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 function.
منابع مشابه
The Noncommutative Wiener Lemma, Linear Independence, and Spectral Properties of the Algebra of Time-frequency Shift Operators
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 proves the algebra contains no compact operators. As a corollary we obtain a special case of the Heil-Ramanathan-Topiwala conjecture regarding linear independence of f...
متن کاملA note on power values of generalized derivation in prime ring and noncommutative Banach algebras
Let $R$ be a prime ring with extended centroid $C$, $H$ a generalized derivation of $R$ and $ngeq 1$ a fixed integer. In this paper we study the situations: (1) If $(H(xy))^n =(H(x))^n(H(y))^n$ for all $x,yin R$; (2) obtain some related result in case $R$ is a noncommutative Banach algebra and $H$ is continuous or spectrally bounded.
متن کاملAn Almost Periodic Noncommutative Wiener’s Lemma
We develop a theory of almost periodic elements in Banach algebras and present an abstract version of a noncommutative Wiener’s Lemma. The theory can be used, for example, to derive some of the recently obtained results in time-frequency analysis such as the spectral properties of the finite linear combinations of time-frequency shifts.
متن کاملPOINT DERIVATIONS ON BANACH ALGEBRAS OF α-LIPSCHITZ VECTOR-VALUED OPERATORS
The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let be a non-emp...
متن کاملOn Ergodic Properties of Convolution Operators Associated with Compact Quantum Groups
Recent results of M. Junge and Q.Xu on the ergodic properties of the averages of kernels in noncommutative L-spaces are applied to the analysis of the almost uniform convergence of operators induced by the convolutions on compact quantum groups. The classical ergodic theory was initially concerned with investigating the limits of iterations (or iterated averages) of certain transformations of a...
متن کامل