The matrix Wiener algebra,WN:=MN(W)of order N＞0,is the matrix algebra formed by N x N matrices whose entries belong to the classical Wiener algebra W of functions with absolutely convergent Fourier series.A block-Toeplitz matrix T(a)=[AAi,j]i,j≥0 is a block semi-infinite matrix such that its blocks Ai,j are finite matrices of order N,Aij=Ar,s whenever i-j=r-s and its entries are the coefficients of the Fourier expansion of the generator a:T → MN(C).Such a matrix can be regarded as a bounded linear operator acting on the direct sum of N copies of L2(T).We show that exp(T(a)))differes from T(exp(a))only in a compact operator with a known bound on its norm.In fact,we prove a slightly more general result:for every entire function f and for every compact operator E,there exists a compact operator F such that f(T(a)+E)=T(f(a))+F.We call these T(a)+E's matrices,the quasi block-Toeplitz matrices,and we show that via a computation-friendly norm,they form a Banach algebra.Our results generalize and are motivated by some recent results of Dario Andrea Bini,Stefano Massei and Beatrice Meini.

Elahe BOLOURCHIAN;Bijan Ahmadi KAKAVANDI

Department of Applied Mathematics,Faculty of Mathematical Sciences,Shahid Beheshti University,Tehran,Iran

数学物理学报（英文版）

[1]Elahe BOLOURCHIAN;Bijan Ahmadi KAKAVANDI-.THE EXPONENTIAL OF QUASI BLOCK-TOEPLITZ MATRICES)[J].数学物理学报（英文版）,2022(03):1018-1034

EXPONENTIAL,QUASI,TOEPLITZ,MATRICES,AAi,Aij,differes,Dario,Bini,Stefano,Massei,Beatrice,Meini

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